Ebook: Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
Author: William Goldman, Greg McShane, George Stantchev
- Tags: Isometrics (Mathematics), Group theory., Automorphisms., Hyperbolic spaces., Free groups.
- Series: Memoirs of the American Mathematical Society Ser.
- Year: 2019
- Publisher: American Mathematical Society
- City: Providence, United States
- Edition: 1
- Language: English
- pdf
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 $kappa _{Phi}^{-1}(k)$.
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