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Relevant bibliographies by topics / Abelianization

Academic literature on the topic 'Abelianization'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Abelianization"

1

SATO, MASATOSHI. "The abelianization of a symmetric mapping class group." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (September 2009): 369–88. http://dx.doi.org/10.1017/s0305004109002576.

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AbstractLet Σg,r be a compact oriented surface of genus g with r boundary components. We determine the abelianization of the symmetric mapping class group (g,r)(p2) of a double unbranched cover p2: Σ2g − 1,2r → Σg,r using the Riemann constant, Schottky theta constant, and the theta multiplier. We also give lower bounds on the order of the abelianizations of the level d mapping class group.

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SATOH, TAKAO. "The abelianization of the congruence IA-automorphism group of a free group." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 2 (March 2007): 239–48. http://dx.doi.org/10.1017/s0305004106009959.

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AbstractWe consider the abelianizations of some normal subgroups of the automorphism group of a finitely generated free group. Let Fn be a free group of rank n. For d ≥ 2, we consider a group consisting the automorphisms of Fn which act trivially on the first homology group of Fn with ${\mathbf Z}$/d${\mathbf Z}$-coefficients. We call it the congruence IA-automorphism group of level d and denote it by IAn,d. Let IOn,d be the quotient group of the congruence IA-automorphism group of level d by the inner automorphism group of a free group. We determine the abelianization of IAn,d and IOn,d for n ≥ 2 and d ≥ 2. Furthermore, for n=2 and odd prime p, we compute the integral homology groups of IA2,p for any dimension.

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Ratcliffe, John G., and Steven T. Tschantz. "Abelianization of space groups." Acta Crystallographica Section A Foundations of Crystallography 65, no. 1 (November 18, 2008): 18–27. http://dx.doi.org/10.1107/s0108767308036222.

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Hausel, Tamás, and Nicholas Proudfoot. "Abelianization for hyperkähler quotients." Topology 44, no. 1 (January 2005): 231–48. http://dx.doi.org/10.1016/j.top.2004.04.002.

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Blachar, Guy, Orit Sela–Ben-David, and Uzi Vishne. "Abelianization of the Cartwright-Steger lattice." Algebra and Discrete Mathematics 34, no. 2 (2022): 176–86. http://dx.doi.org/10.12958/adm1966.

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The Cartwright-Steger lattice is a group whose Cayley graph can be identified with the Bruhat-Tits building of PGLd over a local field of positive characteristic. We give a lower bound on the abelianization of this lattice, and report that the bound is tight in all computationally accessible cases.

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Wehrfritz, B. A. F. "The abelianization of hypercyclic groups." Central European Journal of Mathematics 5, no. 4 (December 2007): 686–95. http://dx.doi.org/10.2478/s11533-007-0030-4.

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Loran, F. "Abelianization of first class constraints." Physics Letters B 547, no. 1-2 (October 2002): 63–68. http://dx.doi.org/10.1016/s0370-2693(02)02734-x.

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Kamgarpour, Masoud. "Stacky abelianization of algebraic groups." Transformation Groups 14, no. 4 (October 31, 2009): 825–46. http://dx.doi.org/10.1007/s00031-009-9067-8.

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Nunes, João P., and Howard J. Schnitzer. "Field Strength Correlators for Two-Dimensional Yang–Mills Theories Over Riemann Surfaces." International Journal of Modern Physics A 12, no. 26 (October 20, 1997): 4743–68. http://dx.doi.org/10.1142/s0217751x9700253x.

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The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

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Dimca, Alexandru, Richard Hain, and Stefan Papadima. "The abelianization of the Johnson kernel." Journal of the European Mathematical Society 16, no. 4 (2014): 805–22. http://dx.doi.org/10.4171/jems/447.

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Dissertations / Theses on the topic "Abelianization"

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Wu, Xiaohong. "Difference sets: extraneous multipliers and Abelianization /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487856076412741.

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Schmäschke, Felix. "Abelianization and Floer homology of Lagrangians in clean intersection." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-223391.

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This thesis is split up into two parts each revolving around Floer homology and quantum cohomology of closed monotone symplectic manifolds. In the first part we consider symplectic manifolds obtained by symplectic reduction. Our main result is that a quantum version of an abelianization formula of Martin holds, which relates the quantum cohomologies of symplectic quotients by a group and by its maximal torus. Also we show a quantum version of the Leray-Hirsch theorem for Floer homology of Lagrangian intersections in the quotient. The second part is devoted to Floer homology of a pair of monotone Lagrangian submanifolds in clean intersection. Under these assumptions the symplectic action functional is degenerated. Nevertheless Frauenfelder defines a version of Floer homology, which is in a certain sense an infinite dimensional analogon of Morse-Bott homology. Via natural filtrations on the chain level we were able to define two spectral sequences which serve as a tool to compute Floer homology. We show how these are used to obtain new intersection results for simply connected Lagrangians in the product of two complex projective spaces. The link between both parts is that in the background the same technical methods are applied; namely the theory of holomorphic strips with boundary on Lagrangians in clean intersection. Since all our constructions rely heavily on these methods we also give a detailed account of this theory although in principle many results are not new or require only straight forward generalizations.

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Kineider, Clarence. "Partial abelianization of GLn-local systems and non-commutative A-coordinates." Electronic Thesis or Diss., Strasbourg, 2023. http://www.theses.fr/2023STRAD059.

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Dans cette thèse, nous avons pour objectif d'étudier les espaces de modules des G-systèmes locaux sur une surface ciliée S pour divers groupes de Lie G. Nous généralisons une construction de Gaiotto-Moore-Neitzke appelée « abélianisation », permettant que cette procédure soit réalisée de manière « partielle ». Le résultat de cette procédure généralisée nous permet de décrire la topologie de sous-espaces ouverts denses à dans l'espace de modules des GL_2n-systèmes locaux, et en collaboration avec Eugen Rogozinnikov, nousavons étendu davantage la procédure d'abélianisation aux systèmes locaux symplectiques, nous permettant de décrire la topologie des sous-espaces ouverts denses à l'intérieur de l'espace de modules des systèmes locaux symplectiques. En particulier, nous décrivons la topologie de l'ensemble des représentations maximales d'un groupe de surface percée dans un groupe symplectique Sp(A, s) sur une algèbre symétrique (A, s).Étant donné les liens étroits entre la construction originale de Gaiotto-Moore-Neitzke et les coordonnées de cluster de Fock-Goncharov, un autre avantage de la construction d'abélianisation généralisée est qu'elle nous aide à définir et étudier une généralisation non-commutative des coordonnées A de Fock-Goncharov. Lorsque G = GL_2n(R), nous montrons que ces coordonnées A non commutatives définissent une représentation de l'algèbre non commutative A_S introduite par Berenstein-Retakh. Ces coordonnées A non commutatives se restreignent également à des coordonnées non commutatives sur l'espace des représentations symplectiques avec un encadrement lagrangien
In this thesis, we aim to study moduli spaces of G-local systems over a ciliated surface S for various Lie groups G. We generalize a construction of Gaiotto-Moore-Neitzke called abelianization, allowing this procedure to be conducted ''partially''. The result of this generalized procedure allow us to describe the topology of open dense subspaces inside the moduli space of GL_2n-local systems, and together with Eugen Rogozinnikov we extended further the abelianization procedure to symplectic local systems, allowing us to describe the topology of open dense subspaces inside the moduli space of symplectic local systems. In particular, we describe the topology of the set of maximal representations of a punctured surface group into a symplectic group Sp(A,s) over a symmetric algebra (A,s). Given the strong relations between the original construction by Gaiotto-Moore-Neitzke andFock-Goncharov cluster coordinates, another benefit of the generalized abelianization construction is that it help us define and study a non-commutative generalization of Fock-Goncharov A-coordinates. When G = GL_2n(R), we show that these non-commutative A-coordinates define a representation of the non-commutative algebra A_S introduced by Berenstein-Retakh. These non-commutative A-coordinates also restrict to non-commutative coordinates on the space of symplectic representations with lagrangian framing

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Schmäschke, Felix [Verfasser], Matthias [Akademischer Betreuer] Schwarz, Matthias [Gutachter] Schwarz, and Urs [Gutachter] Frauenfelder. "Abelianization and Floer homology of Lagrangians in clean intersection / Felix Schmäschke ; Gutachter: Matthias Schwarz, Urs Frauenfelder ; Betreuer: Matthias Schwarz." Leipzig : Universitätsbibliothek Leipzig, 2017. http://d-nb.info/1240847084/34.

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Schmäschke, Felix. "Abelianization and Floer homology of Lagrangians in clean intersection." Doctoral thesis, 2016. https://ul.qucosa.de/id/qucosa%3A15581.

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This thesis is split up into two parts each revolving around Floer homology and quantum cohomology of closed monotone symplectic manifolds. In the first part we consider symplectic manifolds obtained by symplectic reduction. Our main result is that a quantum version of an abelianization formula of Martin holds, which relates the quantum cohomologies of symplectic quotients by a group and by its maximal torus. Also we show a quantum version of the Leray-Hirsch theorem for Floer homology of Lagrangian intersections in the quotient. The second part is devoted to Floer homology of a pair of monotone Lagrangian submanifolds in clean intersection. Under these assumptions the symplectic action functional is degenerated. Nevertheless Frauenfelder defines a version of Floer homology, which is in a certain sense an infinite dimensional analogon of Morse-Bott homology. Via natural filtrations on the chain level we were able to define two spectral sequences which serve as a tool to compute Floer homology. We show how these are used to obtain new intersection results for simply connected Lagrangians in the product of two complex projective spaces. The link between both parts is that in the background the same technical methods are applied; namely the theory of holomorphic strips with boundary on Lagrangians in clean intersection. Since all our constructions rely heavily on these methods we also give a detailed account of this theory although in principle many results are not new or require only straight forward generalizations.:1. Introduction 2. Overview of the main results 2.1. Abelianization . 2.2. Quantum Leray-Hirsch theorem 2.3. Floer homology of Lagrangians in clean intersection 3. Background 3.1. Symplectic geometry . 3.2. Hamiltonian action functional 3.3. Morse homology . 3.4. Floer homology 4. Asymptotic analysis 4.1. Main statement . 4.2. Mean-value inequality . 4.3. Isoperimetric inequality 4.4. Linear theory 4.5. Proofs 5. Compactness 5.1. Cauchy-Riemann-Floer equation . 5.2. Local convergence . 5.3. Convergence on the ends 5.4. Minimal energy . 5.5. Action, energy and index estimates 6. Fredholm Theory 6.1. Banach manifold . 6.2. Linear theory 7. Transversality 7.1. Setup 7.2. R-dependent structures 7.3. R-invariant structures . 7.4. Regular points . 7.5. Floer’s ε-norm . 8. Gluing 8.1. Setup and main statement 8.2. Pregluing . 8.3. A uniform bounded right inverse 8.4. Quadratic estimate 8.5. Continuity of the gluing map 8.6. Surjectivity of the gluing map 8.7. Degree of the gluing map 8.8. Morse gluing . 9. Orientations 9.1. Preliminaries and notation 9.2. Spin structures and relative spin structures 9.3. Orientation of caps 9.4. Linear theory . 10.Pearl homology 10.1. Overview . 10.2. Pearl trajectories . 10.3. Invariance . 10.4. Spectral sequences 11.Proofs of the main results 11.1. Abelianization Theorem 11.2. Quantum Leray-Hirsch Theorem . 12.Applications 12.1. Quantum cohomology of the complex Grassmannian 12.2. Lagrangian spheres in symplectic quotients A. Estimates A.1. Derivative of the exponential map A.2. Parallel Transport A.3. Estimates for strips B. Operators on Hilbert spaces B.1. Spectral gap B.2. Flow operator C. Viterbo index D. Quotients of principal bundles by maximal tori D.1. Compact Lie groups D.2. The cohomology of the quotient of principle bundles by maximal tori

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Book chapters on the topic "Abelianization"

1

Stillwell, John. "Homology Theory and Abelianization." In Graduate Texts in Mathematics, 169–84. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-4372-4_6.

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Herfort, Wolfgang, and Wolfram Hojka. "On the Abelianization of Certain Topologist’s Products." In Groups, Modules, and Model Theory - Surveys and Recent Developments, 351–58. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51718-6_19.

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Weintraub, Steven H. "The abelianization of the theta group in low genus." In Lecture Notes in Mathematics, 382–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0084759.

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Reutenauer, Christophe. "Basics." In From Christoffel Words to Markoff Numbers, 7–8. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0002.

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Definitions and basic results about words: alphabet, length, free monoid, concatenation, prefix, suffix, factor, conjugation, reversal, palindrome, commutative image, periodicity, ultimate periodicity, periodic pattern, infinite words, bi-infinite words, free groups, reduced words, homomorphisms, embedding of a free monoid in a free group, abelianization,matrix of an endomorphism, GL₂(Z), SL₂(Z).

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Reutenauer, Christophe. "Bases and Automorphisms of the Free Group on Two Generators." In From Christoffel Words to Markoff Numbers, 125–42. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0017.

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The chapter begins with a self-contained exposition of the theory of Nielsen on the free groupwith two generators: bases of F(a, b),Nielsen’s criterion for automorphisms of F(a, b), It also coversNielsen’s theoremon abelianization of these automorphisms andWeinbaum’s theorem on representatives of the group of automorphisms modulo the subgroup of inner automorphism. Perrine’s theorem on bases of the derived group of SL2(Z) and Markoff triples is deduced, and a very simple and efficient algorithm for detecting bases of F(a, b) is given (Séébold, Kassel, the author). Positive automorphisms of F(a, b) are characterized (Wen andWen) and shown to coincide with Sturmian morphisms (Mignosi, Séébold).

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Conference papers on the topic "Abelianization"

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Ting, Tan Yee, Nor'ashiqin Mohd Idrus, Rohaidah Masri, Wan Nor Farhana Wan Mohd Fauzi, Nor Haniza Sarmin, and Hazzirah Izzati Mat Hassim. "On the abelianization of all Bieberbach groups of dimension four with symmetric point group of order six." In INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014): Proceedings of the 3rd International Conference on Quantitative Sciences and Its Applications. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4903625.

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