Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane

William Goldman, Greg McShane, George Stantchev, Ser Peow Tan (Autoren)

Buch | Softcover

78 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-3614-8 (ISBN)

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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) := -x^{2} -y^{2} + z^{2} + x y z -2 $ and an area form on the level surfaces $/kappa _{/Phi}^{-1}(k)$.

William Goldman, University of Maryland, College Park, Maryland. Greg McShane, Institut Fourier, Grenoble, France. George Stantchev, University of Maryland, College Park, Maryland. Ser Peow Tan, University of Singapore, Singapore.

Introduction
The rank two free group and its automorphisms
Character varieties and their automorphisms
Topology of the imaginary commutator trace
Generalized Fricke spaces
Bowditch theory
Imaginary trace labelings
Imaginary characters with $k>2$
Imaginary characters with $k<2$
Imaginary characters with $k=2$
Bibliography

Erscheinungsdatum	21.07.2019
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	175 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-3614-0 / 1470436140
ISBN-13	978-1-4704-3614-8 / 9781470436148
Zustand	Neuware