Computational Aspects of Discrete Subgroups of Lie Groups
This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.The major theme deal...
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| Hlavní autoři: | , , |
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Providence, Rhode Island
American Mathematical Society
07.03.2023
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| Vydání: | 1 |
| Edice: | Contemporary Mathematics |
| Témata: | |
| ISBN: | 1470468042, 9781470468040 |
| ISSN: | 0271-4132, 1098-3627 |
| On-line přístup: | Získat plný text |
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- Enumerating Kleinian Groups -- Exploring Lie theory with <sans-serif>GAP</sans-serif> -- Freeness and <inline-formula content-type="math/mathml"> S S </inline-formula>-arithmeticity of rational Möbius groups -- Computability Models: Algebraic, Topological and Geometric Algorithms -- Compact components of planar surface group representations -- Proving infinite index for a subgroup of matrices -- Geometric algorithms for discreteness and faithfulness -- List of problems on discrete subgroups of Lie groups and their computational aspects -- Picard modular groups generated by complex reflections -- Verifying the Straight-and-spaced Condition -- Unipotent Generators for Arithmetic Groups
- 7. Group homomorphisms -- 8. Testing for undistortion. Part I -- 9. Testing for undistortion. Part II -- 10. Testing for nondistortion. Part III -- 11. Selberg's higher rank generalization of Dirichlet domain and the Poincaré Algorithm -- 12. Computational aspects of Anosov subgroups -- Acknowledgment -- References -- List of problems on discrete subgroups of Lie groups and their computational aspects -- 1. Background -- 2. (2,ℤ)-related problems -- 3. (3,ℤ)-related problems -- 4. Problems on higher rank lattices -- 5. Algorithmic problems -- References -- Picard modular groups generated by complex reflections -- 1. Introduction -- 2. Complex hyperbolic space and isometries -- 3. Picard modular groups and complex reflections -- 4. The Hurwitz modular group and quaternionic reflections -- Acknowledgment -- References -- Verifying the Straight-and-spaced Condition -- Introduction -- 1. Background -- 2. Numerical experiments -- 3. The straight-and-spaced condition in higher rank -- Acknowledgments -- References -- Unipotent Generators for Arithmetic Groups -- 1. Introduction -- 2. Preliminaries -- 3. The Case Where is not abelian -- 4. The Case Where is abelian -- Acknowledgments -- References -- Back Cover
- Cover -- Title page -- Contents -- Preface -- Enumerating Kleinian Groups -- 1. Introduction -- 2. Applications and historical context -- 3. Background -- 4. Markings -- 5. Parameter spaces -- 6. Analyzing parameter spaces and elimination criteria -- 7. Computational setup -- 8. Finding useful words -- 9. Arithmetic and computational considerations -- 10. Sanity checking -- References -- Exploring Lie theory with GAP -- 1. Introduction -- 2. Preliminaries -- 3. Reachable elements -- 4. The quotients ₑ -- 5. Closures of nilpotent orbits of ₁₃ -- Acknowledgments -- References -- Freeness and -arithmeticity of rational Möbius groups -- 1. Introduction -- 2. Non-freeness criteria for Möbius groups -- 3. Exploiting Zariski density of Möbius groups -- 4. Experimentation -- Acknowledgments -- References -- Computability Models: Algebraic, Topological and Geometric Algorithms -- 1. Introduction -- 2. Background and Notation -- 3. Computability and Decidability -- 4. Computational models: type of allowed simple steps -- 5. Geometric Algorithms -- 6. Blum-Shub-Smale Machines, BSS Machines -- 7. Symbolic Computation-Computer Algebra -- 8. Bit Computability over the Reals -- 9. (2,ℝ)-decidability: The Teichmüller Space is BSS decidable -- 10. Conclusion -- 11. The Overriding Question -- 12. Acknowledgement -- References -- Compact components of planar surface group representations -- 1. Relative character varieties of surfaces -- 2. The one-holed torus -- 3. The four-holed sphere -- 4. Recent developments -- Acknowledgment -- References -- Proving infinite index for a subgroup of matrices -- References -- Geometric algorithms for discreteness and faithfulness -- 1. Introduction -- 2. Basic hyperbolic geometry -- 3. Hyperbolic bisectors -- 4. Isometries of the hyperbolic space -- 5. Connecting hyperbolic geodesics -- 6. Quasigeodesics