
Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
American Mathematical Society (Publisher)
Will be published approx. on 30. July 2019
Book
Paperback/Softback
78 pages
978-1-4704-3614-8 (ISBN)
Description
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 $\kappa _{\Phi}^{-1}(k)$.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
175 gr
ISBN-13
978-1-4704-3614-8 (9781470436148)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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.
Greg McShane, Institut Fourier, Grenoble, France.
George Stantchev, University of Maryland, College Park, Maryland.
Ser Peow Tan, University of Singapore, Singapore.
Content
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
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