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 $\kappa _{\Phi}^{-1}(k)$.
ISBN: | 9781470436148 |
Publication date: | 30th July 2019 |
Author: | William Goldman, Greg McShane, George Stantchev, Ser Peow Tan |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 78 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Algebra Algebraic geometry Geometry Topology |