Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane (Memoirs of the American Mathematical Society) - Softcover

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

Softcover

ISBN 10: 1470436140 ISBN 13: 9781470436148

Publisher: American Mathematical Society, 2019

Synopsis

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 $\kappa _{\Phi}^{-1}(k)$.

About this title

About the Author

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470436140
• ISBN 13: 9781470436148
• Binding: Paperback
• Number of pages: 78