Dissertations / Theses on the topic 'Homology theory'
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Jacobsson, Magnus. "Khovanov homology and link cobordisms /." Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3765.
Full textMcDougall, Adam Corey. "Relating Khovanov homology to a diagramless homology." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/709.
Full textBrautaset, Olav. "Homology Theory from the Geometric Viewpoint." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15695.
Full textYates, Stuart. "Discrete morse theory and L2 homology /." Title page, abstract and contents only, 1997. http://web4.library.adelaide.edu.au/theses/09SM/09smy34.pdf.
Full textJohnson, Christopher Aaron. "Applications of computational homology." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=621.
Full textJia, Bei. "D-branes and K-homology." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/32039.
Full textMaster of Science
Song, Yongjin. "Hermitian algebraic K-theory and dihedral homology /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487681788252481.
Full textLevikov, Filipp. "L-theory, K-theory and involutions." Thesis, University of Aberdeen, 2013. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=201918.
Full textKaygun, Atabey. "Bialgebra cyclic homology with coefficients." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1107564231.
Full textTitle from first page of PDF file. Document formatted into pages; contains vii, 77 p.; also includes graphics Includes bibliographical references (p. 76-77). Available online via OhioLINK's ETD Center
Frøyshov, Kim A. "On Floer homology and four-manifolds with boundary." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282194.
Full textCooper, Benjamin. "3-dimensional topological field theory and Harrison homology." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3360059.
Full textTitle from first page of PDF file (viewed August 11, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 84-86).
Cheng, Wing Kin. "Euler characteristic structure and weight homology /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20CHENGW.
Full textTovstopyat-Nelip, Lev Igorevich. "Braids, transverse links and knot Floer homology:." Thesis, Boston College, 2019. http://hdl.handle.net/2345/bc-ir:108376.
Full textContact geometry has played a central role in many recent advances in low-dimensional topology; e.g. in showing that knot Floer homology detects the genus of a knot and whether a knot is fibered. It has also been used to show that the unknot, trefoil, and figure eight knot are determined by their Dehn surgeries. An important problem in 3-dimensional contact geometry is the classification of Legendrian and transverse knots. Such knots come equipped with some classical invariants. New invariants from knot Floer homology have been effective in distinguishing Legendrian and transverse knots with identical classical invariants, a notoriously difficult task. The Giroux correspondence allows contact structures to be studied via purely topological constructs called open book decompositions. Transverse links are then braids about these open books, which in turn may be thought of as mapping tori of diffeomorphisms of compact surfaces with boundary having marked points, which we refer to as pointed monodromies. In the first part of this thesis, we investigate properties of the transverse invariant in knot Floer homology, in particular its behavior for transverse closures of pointed monodromies possessing certain dynamical properties. The binding of an open book sits naturally as a transverse link in the supported contact manifold. We prove that the transverse link invariant in knot Floer homology of the binding union any braid about the open book is non-zero. As an application, we show that any pointed monodromy with fractional Dehn twist coefficient greater than one has non-zero transverse invariant, generalizing a result of Plamenevskaya for braids about the unknot. In the second part of this thesis, we define invariants of Legendrian and transverse links in universally tight lens spaces using grid diagrams, generalizing those defined by Ozsvath, Szabo and Thurston. We show that our invariants are equivalent to those defined by Lisca, Ozsvath, Szabo and Stipsicz for Legendrian and transverse links in arbitrary contact 3-manifolds. Our argument involves considering braids about rational open book decompositions and filtrations on knot Floer complexes
Thesis (PhD) — Boston College, 2019
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
Grudskaya, Tatiana. "Computation of homology of low-dimensional spaces." Thesis, Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28800.
Full textThom, Andreas Berthold. "Connective E-theory and bivariant homology for C*-algebras." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968501311.
Full textLauda, Aaron Dean. "Open-closed topological quantum field theory and tangle homology." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.614322.
Full textBoyd, Rachael. "Homology of Coxeter and Artin groups." Thesis, University of Aberdeen, 2018. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=237053.
Full textMattox, Wade. "Homology of Group Von Neumann Algebras." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/28397.
Full textPh. D.
Lee, Ik Jae. "A new generalization of the Khovanov homology." Diss., Kansas State University, 2012. http://hdl.handle.net/2097/14170.
Full textDepartment of Mathematics
David Yetter
In this paper we give a new generalization of the Khovanov homology. The construction begins with a Frobenius-algebra-like object in a category of graded vector-spaces with an anyonic braiding, with most of the relations weaken to hold only up to phase. The construction of Khovanov can be adapted to give a new link homology theory from such data. Both Khovanov's original theory and the odd Khovanov homology of Oszvath, Rassmusen and Szabo arise from special cases of the construction in which the braiding is a symmetry.
Goedecke, Julia. "Three viewpoints on semi-abelian homology." Thesis, University of Cambridge, 2009. https://www.repository.cam.ac.uk/handle/1810/224397.
Full textMukherjee, Sujoy. "On Skein Modules and Homology Theories Related to Knot Theory." Thesis, The George Washington University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13810465.
Full textClassical knot theory is the study of simple closed curves in three dimensional space. The dissertation studies algebraic structures related to and motivated by knot theory. Since the first half of 1990, several homology theories have been defined for quandles and, more generally, for shelves whose axioms are motivated by the Reidemeister moves in knot theory. The second chapter of the dissertation studies these homology theories. For rack homology, one of the theorems assert that any finite Abelian group can appear as a torsion subgroup in the rack homology of some quandle. Furthermore, the second quandle homology of quasigroup Alexander quandles is expressed in terms of exterior algebras. Finally, the role of the associativity axiom in the category of self distributive algebraic structures is studied from the viewpoint of the homology theories. One of the results in this discussion explicitly computes the rack homology of shelves with a right fixed element.
Associative shelves form a very useful collection of algebraic structures when comparing the homology theories for shelves and semigroups. Examples of such homology theories include group homology, Hochschild homology, and multi term homology. However, from the perspective of self distributivity, rack and one term homology prove not to be very useful as demonstrated in Chapter two. The third chapter of the dissertation introduces a new homology theory to take care of this issue. In fact, this homology theory works for the family of the so-called quasibands which contain the collection of associative shelves. A theorem in this part of the dissertation computes the second homology group of finite semilattices which are also examples of quasibands. Moreover, the relation between this homology theory and Temperley-Lieb algebras is established.
The third part of the dissertation focuses on Khovanov homology. In particular, the main goal in this part is to study torsion in Khovanov homology. Z2 torsion in Khovanov homology is much better understood than any other torsion. Three years ago, only a finite number of examples of knots and prime links with non Z2 torsion in their Khovanov homology were known. It was also known that knots and links with thin Khovanov homology can contain only Z2 torsion. The work on Khovanov homology in the dissertation introduces the first known examples of infinite families of knots and prime links with non Z 2 torsion in their Khovanov homology. More specifically, infinite families of knots and prime links containing Z3, Z 4, Z5, Z7, and Z8 torsion in their Khovanov homology are introduced. The aforementioned results assert that given some reasonably small torsion group, there are `many' examples of knots and links with the given torsion subgroup in their Khovanov homology. The latter half of this study addresses the `large' side, meaning, methods of finding knots and links with `large' torsion groups in their Khovanov homology. To this end, links with even torsion of order 2s, for 0 < s < 24, in their Khovanov homology are introduced. In the case of odd order, knots and links with Z9, Z25, and Z27 torsion in their Khovanov homology are introduced. These results and discoveries are used to resolve all but one part of the Przytycki-Sazdanović braid conjecture.
The final part of the dissertation is motivated by the elegant product-to-sum formula of Frohman and Gelca for multiplying curves in the Kauffman bracket skein algebra of the thickened torus. After comparing the Kauffman bracket skein algebra of the thickened four-holed sphere with the Kauffman bracket skein algebra of the thickened torus, formulas for multiplying curves in some special families are discussed. Following this, an algorithm to multiply any two curves in the Kauffman bracket skein algebra of the thickened four-holed sphere is described.
Masters, Joseph David. "Lengths and homology of hyperbolic 3-manifolds /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
Full textHubbard, Diana D. "Properties and applications of the annular filtration on Khovanov homology." Thesis, Boston College, 2016. http://hdl.handle.net/2345/bc-ir:106791.
Full textThe first part of this thesis is on properties of annular Khovanov homology. We prove a connection between the Euler characteristic of annular Khovanov homology and the classical Burau representation for closed braids. This yields a straightforward method for distinguishing, in some cases, the annular Khovanov homologies of two closed braids. As a corollary, we obtain the main result of the first project: that annular Khovanov homology is not invariant under a certain type of mutation on closed braids that we call axis-preserving. The second project is joint work with Adam Saltz. Plamenevskaya showed in 2006 that the homology class of a certain distinguished element in Khovanov homology is an invariant of transverse links. In this project we define an annular refinement of this element, kappa, and show that while kappa is not an invariant of transverse links, it is a conjugacy class invariant of braids. We first discuss examples that show that kappa is non-trivial. We then prove applications of kappa relating to braid stabilization and spectral sequences, and we prove that kappa provides a new solution to the word problem in the braid group. Finally, we discuss definitions and properties of kappa in the reduced setting
Thesis (PhD) — Boston College, 2016
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
Durusoy, Daniel Selahi. "Heegaard Floer homology of certain 3-manifolds and cobordism invariants." Diss., Connect to online resource - MSU authorized users, 2008.
Find full textPASINI, FEDERICO WILLIAM. "Classifying spaces for knots: new bridges between knot theory and algebraic number theory." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/129230.
Full textBoily, Christian M. "Homological flows & star formation." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321079.
Full textHeß, Alexander [Verfasser]. "Factorable Monoids : Resolutions and Homology via Discrete Morse Theory / Alexander Heß." Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1044081376/34.
Full textHesselmann, Sabine. "Zur Torsion der Kohomologie S-arithmetischer Gruppen." Bonn : [s.n.], 1993. http://catalog.hathitrust.org/api/volumes/oclc/31482302.html.
Full textAdhikari, S. Prashanth. "Torsion in the homology of the general linear group for a ring of algebraic integers /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5770.
Full textHarris, Julianne S. "On the mod 2 general linear group homology of totally real number rings /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5812.
Full textWatson, Greg M. "Computation of homology and an application to the conley index." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/29916.
Full textTram, Heather. "Khovanov Homology as an Generalization of the Jones Polynomial in Kauffman Terms." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/theses/1987.
Full textWienhard, Anna Katharina. "Bounded cohomology and geometry." Bonn : Mathematisches Institut der Universität, 2004. http://catalog.hathitrust.org/api/volumes/oclc/62768224.html.
Full textWeselmann, Uwe. "Kohomologische Kongruenzen zwischen automorphen Darstellungen von GL₂." Bonn : [s.n.], 1993. http://catalog.hathitrust.org/api/volumes/oclc/31445704.html.
Full textSo, Bing-kwan. "On some examples of Poisson homology and cohomology analytic and lie theoretic approaches /." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B3617063X.
Full text馮淑貞 and Suk-ching Fung. "Asymptotic vanishing theorem of cohomology groups on compact quotientsof the unit ball." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31220848.
Full textSo, Bing-kwan, and 蘇鈵鈞. "On some examples of Poisson homology and cohomology: analytic and lie theoretic approaches." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B3617063X.
Full textPearson, Kelly Jeanne. "Cohomology of the Orlik-Solomon algebras." [Eugene, Or. : University of Oregon Library System], 2000. http://libweb.uoregon.edu/UOTheses/2000/pearsonk00.pdf.
Full textFung, Suk-ching. "Asymptotic vanishing theorem of cohomology groups on compact quotients of the unit ball /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20667991.
Full textAntal, Tamás. "Cyclic cohomological computations for the Connes-Moscovici-Kreimer Hopf algebras." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1092777186.
Full textKahle, Matthew. "Topology of random simplicial complexes and phase transitions for homology /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5809.
Full textRüschoff, Christian [Verfasser], and Otmar [Akademischer Betreuer] Venjakob. "Relative algebraic K-theory and algebraic cyclic homology / Christian Rüschoff ; Betreuer: Otmar Venjakob." Heidelberg : Universitätsbibliothek Heidelberg, 2016. http://d-nb.info/1180737873/34.
Full textBoquet, Grant Michael. "Multidimensional Behavioral Complexes." Thesis, Virginia Tech, 2008. http://hdl.handle.net/10919/31528.
Full textMaster of Science
Heistercamp, Muriel. "The Weinstein conjecture with multiplicities on spherizations." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209882.
Full textL'existence d'une orbite orbite fermée du flot de Reeb sur S fut annoncée par Weinstein dans sa conjecture en 1978. Indépendamment, Weinstein et Rabinowitz ont montré l'existence d'une orbite fermée sur les hypersurfaces de type étoilées dans l'espace réel de dimension 2n. Sous les hypothèses précédentes, l'existence d'une orbite fermée fut démontrée par Hofer et Viterbo. Dans le cas particulier du flot géodésique, l'existence de plusieurs orbites fermées fut notamment étudiée par Gromov, Paternain et Paternain-Petean. Dans cette thèse, ces résultats sont généralisés.
Les résultats principaux de cette thèse montrent que la structure topologique de la variété M implique, pour toute hypersurface étoilée fibre par fibre, l'existence de beaucoup d'orbites fermées du flot de Reeb. Plus précisément, une borne inférieure de la croissance du nombre d'orbites fermées du flot de Reeb en fonction de leur période est mise en évidence. /
Let M be a smooth closed manifold and denote by T*M the cotangent bundle over M endowed with its usual symplectic structure induced by the Liouville form. A hypersurface S of T*M is said to be fiberwise starshaped if for each point q in M the intersection Sq of S with the fiber at q bounds a domain starshaped with respect to the origin 0q in T*qM. There is a flow naturally associated to S, generated by the unique Reeb vector field R along S ,the Reeb flow.
The existence of one closed orbit was conjectured by Weinstein in 1978 in a more general setting. Independently, Weinstein and Rabinowitz established the existence of a closed orbit on star-like hypersurfaces in the 2n-dimensional real space. In our setting the Weinstein conjecture without the assumption was proved in 1988 by Hofer and Viterbo. The existence of many closed orbits has already been well studied in the special case of the geodesic flow, for example by Gromov, Paternain and Paternain-Petean. In this thesis we will generalize their results.
The main result of this thesis is to prove that the topological structure of $M$ forces, for all fiberwise starshaped hypersurfaces S, the existence of many closed orbits of the Reeb flow on S. More precisely, we shall give a lower bound of the growth rate of the number of closed Reeb-orbits in terms of their periods.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
Kühnlein, Stefan. "Kohomologie spezieller S-arithmetischer Gruppen und Modulformen." Bonn : [s.n.], 1994. http://catalog.hathitrust.org/api/volumes/oclc/31760587.html.
Full textHolmstrom, Andreas. "Arakelov motivic cohomology." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607895.
Full textMembrillo-Hernandez, Fausto Humberto. "Homological properties of finite-dimensional algebras." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670284.
Full textKnapp, Adam C. "Computations of Floer homology and gauge theoretic invariants for Montesinos twins." Diss., Connect to online resource - MSU authorized users, 2008.
Find full textAgerberg, Jens. "Statistical Learning and Analysis on Homology-Based Features." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-273581.
Full textStable rank har föreslagits som en sammanfattning på datanivå av resultatet av persistent homology, en metod inom topologisk dataanalys. I detta examensarbete utvecklar vi metoder inom statistisk analys och maskininlärning baserade på stable rank. Eftersom stable rank kan ses som en avbildning i ett Hilbertrum kan en kärna konstrueras från inre produkten i detta rum. Först undersöker vi denna kärnas egenskaper när den används inom ramen för maskininlärningsmetoder som stödvektormaskin (SVM). Därefter, med grund i teorin för inbäddning av sannolikhetsfördelningar i reproducing kernel Hilbertrum, undersöker vi hur kärnan kan användas för att utveckla ett test för statistisk hypotesprövning. Slutligen, som ett alternativ till metoder baserade på kärnor, utvecklas en avbildning i ett euklidiskt rum med optimerbara parametrar, som kan användas som ett ingångslager i ett neuralt nätverk. Metoderna utvärderas först på syntetisk data. Vidare utförs ett statistiskt test på OASIS, ett öppet dataset inom neuroradiologi. Slutligen utvärderas metoderna på klassificering av grafer, baserat på ett dataset insamlat från Reddit.
QC 20200523
Rada, Ion Kolster Manfred. "The Lichtenbaum conjecture at the prime 2 /." *McMaster only, 2002.
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