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Relevant bibliographies by topics / Topological invariants

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Academic literature on the topic 'Topological invariants'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Topological invariants"

1

HATAKENAKA, ERI. "Invariants of 3-manifolds derived from covering presentations." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 2 (May 10, 2010): 263–95. http://dx.doi.org/10.1017/s0305004110000198.

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AbstractBy a covering presentation of a 3-manifold, we mean a labelled link (i.e., a link with a monodromy representation), which presents the 3-manifold as the simple 4-fold covering space of the 3-sphere branched along the link with the given monodromy. It is known that two labelled links present a homeomorphic 3-manifold if and only if they are related by a finite sequence of some local moves. This paper presents a method for constructing topological invariants of 3-manifolds based on their covering presentations. The proof of the topological invariance is shown by verifying the invariance under the local moves. As an example of such invariants, we present the Dijkgraaf–Witten invariant of 3-manifolds.

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Kaufmann, Ralph M., Dan Li, and Birgit Wehefritz-Kaufmann. "Notes on topological insulators." Reviews in Mathematical Physics 28, no. 10 (November 2016): 1630003. http://dx.doi.org/10.1142/s0129055x1630003x.

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This paper is a survey of the [Formula: see text]-valued invariant of topological insulators used in condensed matter physics. The [Formula: see text]-valued topological invariant, which was originally called the TKNN invariant in physics, has now been fully understood as the first Chern number. The [Formula: see text] invariant is more mysterious; we will explain its equivalent descriptions from different points of view and provide the relations between them. These invariants provide the classification of topological insulators with different symmetries in which K-theory plays an important role. Moreover, we establish that both invariants are realizations of index theorems which can also be understood in terms of condensed matter physics.

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Ohtsuki, Tomotada. "Invariants of 3-manifolds derived from universal invariants of framed links." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 2 (March 1995): 259–73. http://dx.doi.org/10.1017/s0305004100073102.

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Reshetikhin and Turaev [10] gave a method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra (e.g. a quantum group Uq(sl2)) using finite-dimensional representations of it. In this paper we give another independent method to construct a topological invariant of compact oriented 3-manifolds from a ribbon Hopf algebra via universal invariants of framed links without using representations of the algebra. For Uq(sl2) these two methods give different invariants of 3-manifolds.

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Meilhan, Jean-Baptiste, and Sakie Suzuki. "The universal sl2 invariant and Milnor invariants." International Journal of Mathematics 27, no. 11 (October 2016): 1650090. http://dx.doi.org/10.1142/s0129167x16500907.

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The universal [Formula: see text] invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the [Formula: see text]-adic completed tensor powers of the quantized enveloping algebra of [Formula: see text]. In this paper, we exhibit explicit relationships between the universal [Formula: see text] invariant and Milnor invariants, which are classical invariants generalizing the linking number, providing some new topological insight into quantum invariants. More precisely, we define a reduction of the universal [Formula: see text] invariant, and show how it is captured by Milnor concordance invariants. We also show how a stronger reduction corresponds to Milnor link-homotopy invariants. As a byproduct, we give explicit criterions for invariance under concordance and link-homotopy of the universal [Formula: see text] invariant, and in particular for sliceness. Our results also provide partial constructions for the still-unknown weight system of the universal [Formula: see text] invariant.

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Tur, A. V., and V. V. Yanovsky. "Invariants in dissipationless hydrodynamic media." Journal of Fluid Mechanics 248 (March 1993): 67–106. http://dx.doi.org/10.1017/s0022112093000692.

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We propose a general geometric method of derivation of invariant relations for hydrodynamic dissipationless media. New dynamic invariants are obtained. General relations between the following three types of invariants are established, valid in all models: Lagrangian invariants, frozen-in vector fields and frozen-in co-vector fields. It is shown that frozen-in integrals form a Lie algebra with respect to the commutator of the frozen fields. The relation between frozen-in integrals derived here can be considered as the Backlund transformation for hydrodynamic-type systems of equations. We derive an infinite family of integral invariants which have either dynamic or topological nature. In particular, we obtain a new type of topological invariant which arises in all hydrodynamic dissipationless models when the well-known Moffatt invariant vanishes.

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KRIEGER, WOLFGANG. "On a syntactically defined invariant of symbolic dynamics." Ergodic Theory and Dynamical Systems 20, no. 2 (April 2000): 501–16. http://dx.doi.org/10.1017/s0143385700000249.

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A partially ordered set that is invariantly associated to a subshift is constructed. A property of subshifts, also an invariant of topological conjugacy, is described. If this property is present in a subshift then the constructed partially ordered set is a partially ordered semigroup (with zero). In the description of these invariants the notion of context is instrumental.

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ZHANG, R. B. "QUANTUM SUPERGROUPS AND TOPOLOGICAL INVARIANTS OF THREE-MANIFOLDS." Reviews in Mathematical Physics 07, no. 05 (July 1995): 809–31. http://dx.doi.org/10.1142/s0129055x95000311.

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The Reshetikhin-Turaev approach to topological invariants of three-manifolds is generalized to quantum supergroups. A general method for constructing three-manifold invariant is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, Uq(gl(2|1)) at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.

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Wang, Zhong, Xiao-Liang Qi, and Shou-Cheng Zhang. "Equivalent topological invariants of topological insulators." New Journal of Physics 12, no. 6 (June 17, 2010): 065007. http://dx.doi.org/10.1088/1367-2630/12/6/065007.

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CHO, YONG SEUNG. "GENERATING SERIES FOR SYMMETRIC PRODUCT SPACES." International Journal of Geometric Methods in Modern Physics 09, no. 05 (July 3, 2012): 1250045. http://dx.doi.org/10.1142/s0219887812500454.

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We consider the symmetric product spaces of closed manifolds. We introduce some geometric invariants and the topological properties of symmetric product spaces via the symmetric invariant ones of product spaces and apply to Gromov–Witten invariants. We examine the symmetric product spaces of the complex projective line, their Gromov–Witten invariants and compute the generating series induced by their Gromov–Witten invariants.

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Pattabiraman, K., M. Kameswari, and M. Seenivasan. "Generalized Version of <i>ISI</i> Invariant for some Molecular Structures." Materials Science Forum 1048 (January 4, 2022): 221–26. http://dx.doi.org/10.4028/www.scientific.net/msf.1048.221.

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Degree related topological invariants are the bygone and most victorioustype of graph invariants so far. In this article, we are interested in finding the generalized inverse indeg invariant of the nanostar dendrimers D[r],fullerene dendrimerNS4[r], and polymer dendrimerNS5[r]. Keywords: nanotubes; inverse indeg invariant; nanostar dendrimers; fullerene dendrimer; polymer dendrimer

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Dissertations / Theses on the topic "Topological invariants"

1

Metzler, David S. (David Scott). "Topological invariants of symplectic quotients." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43933.

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Mayer, Christoph. "Topological link invariants of magnetic fields." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969161964.

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Larsen, Nicholas Guy. "A New Family of Topological Invariants." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6757.

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We define an extension of the nth homotopy group which can distinguish a larger class of spaces. (E.g., a converging sequence of disjoint circles and the disjoint union of countably many circles, which have isomorphic fundamental groups, regardless of choice of basepoint.) We do this by introducing a generalization of homotopies, called component-homotopies, and defining the nth extended homotopy group to be the set of component-homotopy classes of maps from compact subsets of (0,1)n into a space, with a concatenation operation. We also introduce a method of tree-adjoinment for "connecting" disconnected metric spaces and show how this method can be used to calculate the extended homotopy groups of an arbitrary metric space.

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Woolf, Jonathan. "Some topological invariants of singular symplectic quotients." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299436.

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Roberts, Justin Deritter. "Quantum invariants via skein theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319336.

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Zach, Matthias [Verfasser]. "Topological invariants of isolated determinantal singularities / Matthias Zach." Hannover : Technische Informationsbibliothek (TIB), 2017. http://d-nb.info/1150664274/34.

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Brunnbauer, Michael. "Topological properties of asymptotic invariants and universal volume bounds." Diss., lmu, 2008. http://nbn-resolving.de/urn:nbn:de:bvb:19-87504.

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Mukherjee, Devarshi [Verfasser]. "Topological Invariants for Non-Archimedean Bornological Algebras / Devarshi Mukherjee." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2020. http://d-nb.info/121973179X/34.

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Guerville, Benoît. "Invariants Topologiques d'Arrangements de droites." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3033/document.

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Cette thèse est le point d’intersection entre deux facettes de l’étude des arrangements de droites : la combinatoire et la topologie. Dans une première partie nous avons étudié l’inclusion de la variété bord dans le complémentaire d’un arrangement. Nous avons ainsi généralisé le résultat d’E. Hironaka au cas de tous les arrangements complexes. Pour contourner les problèmes provenant des arrangements non réels, nous avons étudié le diagramme de câblage, dit wiring diagram, qui code la monodromie de tresses sous forme de tresse singulière. Pour pouvoir l'utiliser, nous avons implémenté un programme sur Sage permettant de calculer ce diagramme en fonction des équations de l’arrangement. Cela nous a permis de d’obtenir deux descriptions explicites de l’application induite par l’inclusion de la variété bord dans le complémentaire sur les groupes fondamentaux. Nous obtenons ainsi deux nouvelles présentations du groupe fondamental du complémentaire d’un arrangement. L’une d’entre elle généralise le théorème de R. Randell au cas des arrangements complexes. Pour continuer ces travaux, nous avons étudié l’application induite par l’inclusion sur le premier groupe d’homologie. Nous obtenons deux descriptions simples de cette application. En s’inspirant des travaux de J.I. Cogolludo, nous décrivons une décomposition canonique du premier groupe d’homologie de la variété bord comme produit de la 1-homologie et de la 2-cohomologie du complémentaire, ainsi qu'un isomorphisme entre la 2-cohomologie du complémentaire et la 1-homologie du graphe d’incidence. Dans la seconde partie de notre travail nous nous sommes intéressés à l’étude des caractères du groupe fondamental du complémentaire. Nous partons des résultats obtenus par E. Artal sur le calcul de la profondeur d’un caractère. Cette profondeur peut être décomposée en un terme projectif et un terme quasi-projectif. Un algorithme pour calculer la partie projective a été donné par A. Libgober. Les travaux de E. Artal concernent la partie quasi-projective. Il a obtenu une méthode pour la calculer en fonction de l’image de certains cycles particuliers du complémentaire par le caractère. En utilisant les résultats obtenus dans la première partie, nous avons obtenu un algorithme complet permettant le calcul de la profondeur quasi-projective d’un caractère. A travers l’étude de cet algorithme, nous avons obtenu une condition combinatoire pour admettre une profondeur quasi-projective potentiellement non combinatoire. Nous avons ainsi défini la notion de caractère inner-cyclic . Cette notion nous a permis de formuler des conditions fortes sur la combinatoire pour qu’un arrangement n’ait que des caractères de profondeur quasi-projective nulle. Enfin pour diminuer le nombre d’exemples à considérer nous avons introduit la notion de combinatoire première. Si une combinatoire ne l’est pas, alors les variétés caractéristiques de ses réalisations sont définies par celles d’un arrangement avec moins de droites. En parallèle à cette étude, nous avons observé que la composition de l’application induite par l’inclusion sur le premier groupe d’homologie avec un caractère nous fournit un invariant topologique de l'arrangement obtenu en désingularisant les points multiples (blow-up). De plus, nous montrons que cet invariant n’est pas de nature combinatoire. Il nous a ainsi permis de découvrir deux nouvelles nc-paires de Zariski
This thesis is the intersection point between the two facets of the study of line arrangements: combinatorics and topology. In the first part, we study the inclusion of the boundary manifold in the complement of an arrangement. We generalize the results of E. Hironaka to the case of any complex line arrangement. To get around the problems due to the case of non complexified real arrangement, we study the braided wiring diagram. We develop a Sage program to compute it from the equation of the complex line arrangement. This diagram allows to give two explicit descriptions of the map induced by the inclusion on the fundamental groups. From theses descriptions, we obtain two new presentations of the fundamental group of the complement. One of them is a generalization of the R. Randell Theorem to any complex line arrangement. In the next step of this work, we study the map induced by the inclusion on the first homology group. Then we obtain two simple descriptions of this map. Inspired by ideas of J.I. Cogolludo, we give a canonical description of the homology of the boundary manifold as the product of the 1-homology with the 2-cohomology of the complement. Finally, we obtain an isomorphism between the 2-cohomology of the complement with the 1-homology of the incidence graph of the arrangement. In the second part, we are interested by the study of character on the group of the complement. We start from the results of E. Artal on the computation of the depth of a character. This depth can be decomposed into a projective term and a quasi-projective term, vanishing for characters that ramify along all the lines. An algorithm to compute the projective part is given by A. Libgober. E. Artal focuses on the quasi-projective part and gives a method to compute it from the image by the character of certain cycles of the complement. We use our results on the inclusion map of the boundary manifold to determine these cycles explicitly. Combined with the work of E. Artal we obtain an algorithm to compute the quasi-projective depth of any character. From the study of this algorithm, we obtain a strong combinatorial condition on characters to admit a quasi-projective depth potentially not determined by the combinatorics. With this property, we define the inner-cyclic characters. From their study, we observe a strong condition on the combinatorics of an arrangement to have only characters with null quasi-projective depth. Related to this, in order to reduce the number of computations, we introduce the notion of prime combinatorics. If a combinatorics is not prime, then the characteristics varieties of its realizations are completely determined by realization of a prime combinatorics with less line. In parallel, we observe that the composition of the map induced by the inclusion with specific characters provide topological invariants of the blow-up of arrangements. We show that the invariant captures more than combinatorial information. Thereby, we detect two new examples of nc-Zariski pairs

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Sweeney, Andrew. "A Study of Topological Invariants in the Braid Group B2." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3407.

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The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the Temperley-Lieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group Bn is the set of braids on n strands along with the binary operation of concatenation. This thesis also shows results of the relationship between the closure of a product of braids in B2 and the connected sum of the closure of braids in B2. Results on the topological invariant of tricolorability of closed braids in B2 and (2,n) torus links along with their obverses are presented as well.

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Books on the topic "Topological invariants"

1

Lipman, Joseph. Topological invariants of quasi-ordinary singularities. Providence, R.I., USA: American Mathematical Society, 1988.

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Fredholm Structures, topological invariants and applications. Springfield, MO: American Institute of Mathematical Sciences, 2009.

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Szafraniec, Zbigniew. Topological invariants of real analytic sets. Gdańsk: Uniwersytet Gdański, 1993.

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Kaminker, Jerome, ed. Geometric and Topological Invariants of Elliptic Operators. Providence, Rhode Island: American Mathematical Society, 1990. http://dx.doi.org/10.1090/conm/105.

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I, Arnolʹd V. Topological invariants of plane curves and caustics. Providence, R.I: American Mathematical Society, 1994.

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Prodan, Emil, and Hermann Schulz-Baldes. Bulk and Boundary Invariants for Complex Topological Insulators. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29351-6.

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Topological methods in Galois representation theory. New York: Wiley, 1989.

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An introduction to invariants and moduli. Cambridge, U.K: Cambridge University Press, 2003.

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Gabriel, Patrick. Ensemble d'invariants pour les produits croisés de Anzai. Montrouge, France: Société mathématique de France, 1991.

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Functorial knot theory: Categories of tangles, coherence, categorical deformations, and topological invariants. Singapore: World Scientific, 2001.

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Book chapters on the topic "Topological invariants"

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Bracci, Filippo, Manuel D. Contreras, and Santiago Díaz-Madrigal. "Topological Invariants." In Springer Monographs in Mathematics, 541–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36782-4_18.

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Webb, Gary. "Topological Invariants." In Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws, 69–113. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72511-6_6.

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Carter, Scott, Seiichi Kamada, and Masahico Saito. "Topological Invariants." In Surfaces in 4-Space, 77–121. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-10162-9_3.

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Shen, Shun-Qing. "Topological Invariants." In Springer Series in Solid-State Sciences, 47–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32858-9_4.

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Shen, Shun-Qing. "Topological Invariants." In Springer Series in Solid-State Sciences, 51–79. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4606-3_4.

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Monk, J. Donald. "Topological density." In Cardinal Invariants on Boolean Algebras, 107–15. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0346-0334-8_6.

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Monk, J. Donald. "Topological Density." In Cardinal Invariants on Boolean Algebras, 219–35. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0730-2_6.

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Gresch, Dominik, and Alexey Soluyanov. "Calculating Topological Invariants with Z2Pack." In Topological Matter, 63–92. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76388-0_3.

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Némethi, András. "Topological Invariants. The Seiberg–Witten Invariant." In Normal Surface Singularities, 433–99. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06753-2_9.

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Prodan, Emil. "Applications II: Topological Invariants." In SpringerBriefs in Mathematical Physics, 109–18. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55023-7_9.

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Conference papers on the topic "Topological invariants"

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Segoufin, Luc, and Victor Vianu. "Querying spatial databases via topological invariants." In the seventeenth ACM SIGACT-SIGMOD-SIGART symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/275487.275498.

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St-Jean, P., A. Dauphin, P. Massignan, B. Real, O. Jamadi, M. Milicevic, A. Lemaitre, et al. "Measuring topological invariants in polaritonic lattices." In 2021 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC). IEEE, 2021. http://dx.doi.org/10.1109/cleo/europe-eqec52157.2021.9542737.

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REYES, ANDRES. "QUANTUM HALL CONDUCTIVITY AND TOPOLOGICAL INVARIANTS." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810571_0012.

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Hafezi, Mohammad. "Measuring Topological Invariants in Photonic Systems." In Integrated Photonics Research, Silicon and Nanophotonics. Washington, D.C.: OSA, 2015. http://dx.doi.org/10.1364/iprsn.2015.is3a.1.

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Henselman, Gregory, and Pawel Dlotko. "Combinatorial invariants of multidimensional topological network data." In 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2014. http://dx.doi.org/10.1109/globalsip.2014.7032235.

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Parto, Midya, Christian Leefmans, James Williams, Franco Nori, and Alireza Marandi. "Measuring Topological Invariants within Dissipatively-Coupled Lattices." In CLEO: QELS_Fundamental Science. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.ftu4j.1.

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We demonstrate Bloch oscillations in a dissipatively-coupled network of time-multiplexed resonators, and experimentally measure the topological invariants in open systems. This reveals the complex interplay between topology and dissipation with potential applications in quantum/classical photonics.

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Idrees, Muhammad, Hongbin Ma, Numan Amin, Abdul Rauf Nizami, Zaffar Iqbal, and Saiid Ali. "Several Topological Invariants of Generalized Möbius Ladder." In 2018 37th Chinese Control Conference (CCC). IEEE, 2018. http://dx.doi.org/10.23919/chicc.2018.8484170.

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Sato, Nobuya, and Michihisa Wakui. "(2+1)–dimensional topological quantum field theory with a Verlinde basis and Turaev–Viro–Ocneanu invariants of 3–manifolds." In Invariants of Knots and 3--manifolds. Mathematical Sciences Publishers, 2002. http://dx.doi.org/10.2140/gtm.2002.4.281.

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Tang, Xinming, Wolfgang Kainz, and Hui Zhang. "Some Topological Invariants and a Qualitative Topological Relation Model between Fuzzy Regions." In Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007). IEEE, 2007. http://dx.doi.org/10.1109/fskd.2007.522.

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Park, Tae Gwan, Junho Park, Eon Taek Oh, Hong Ryeol Na, Seung-Hyun Chun, Sunghun Lee, and Fabian Rotermund. "Ultrafast switching of topological invariants by light-driven interlayer vibrations." In CLEO: Fundamental Science. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cleo_fs.2023.ff2g.2.

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We investigate the high-speed topological phase transition driven by photoinduced interlayer vibrations at ambient conditions (room temperature and normal pressure). By employing ultrafast optical and THz spectroscopy, which enables us possible to study interlayer vibrations through photoelastic effects and topological surface state leading to low-energy conductivity in topological insulator Bi2Se3, we found that the interlayer vibrational mode, which originated from the confinement of photoinduced longitudinal strain waves, can drive the topological phase switching from topological insulator toward normal insulator. Our observations provide fundamental insights into nanomechanical interaction between lattice-topological phase for possible optoelectronic and spintronic applications based on all-optical topological phase switching at ultrafast timescales.

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Reports on the topic "Topological invariants"

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Makaruk, Hanna, and Robert Owczarek. Topological Invariant of Manifolds in Sławianowski’s Field Theory. Office of Scientific and Technical Information (OSTI), July 2022. http://dx.doi.org/10.2172/1876771.

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