| Description |
1 online resource (92 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1249 |
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Memoirs of the American Mathematical Society ; no. 1249.
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| Contents |
1. Introduction -- 2. The rank two free group and its automorphisms -- 3. Character varieties and their automorphisms -- 4. Topology of the imaginary commutator trace -- 5. Generalized Fricke spaces -- 6. Bowditch theory -- 7. Imaginary trace labelings -- 8. Imaginary characters with k>2 -- 9. Imaginary characters with k<2 -- 10. Imaginary characters with k=2 |
| Summary |
The automorphisms of a two-generator free group \mathsf F_2 acting on the space of orientation-preserving isometric actions of \mathsf F_2 on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group \Gamma on \mathbb R ̂3 by polynomial automorphisms preserving the cubic polynomial \kappa _\Phi (x, y, z) := -x̂{2} -ŷ{2} + ẑ{2} + x y z -2 and an area form on the level surfaces \kappa _{\Phi}̂{-1}(k) |
| Notes |
Keywords: character variety, free group, outer automorphism group, hyperbolic surface, nonorientable surface, hyperbolic surface, conical singularity, Nielsen transformation, ergodic equivalence relation, Fricke space, mapping class group, tree, Markoff map |
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"May 2019, volume 259, number 1249 (sixth of 8 numbers)." |
| Bibliography |
Includes bibliographical references (pages 77-78) |
| Notes |
Online resource; title from PDF title page (viewed August 27, 2019) |
| Subject |
Free groups.
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Automorphisms.
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Group theory.
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Isometrics (Mathematics)
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Hyperbolic spaces.
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Teoría de grupos
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Isometría (Matemáticas)
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Ecuaciones diferenciales hiperbólicas
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Automorfismos
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Automorphisms
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Free groups
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Group theory
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Hyperbolic spaces
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Isometrics (Mathematics)
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| Form |
Electronic book
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| Author |
McShane, Greg, 1966- author.
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Stantchev, George, author.
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Tau, Ser Peow, author
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| ISBN |
1470452537 |
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1470436140 |
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9781470436148 |
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9781470452537 |
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