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

Automorphisms of Two-generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane (Memoirs of the American Mathematical Society)
by: William Goldman (Author),Greg Mcshane(Author),George Stantchev(Author),Ser Peow Tan(Author)&1more
Publisher: Amer Mathematical Society
Publication Date: 2019/6/14
Language: English
Print Length: 78 pages
ISBN-10: 1470436140
ISBN-13: 9781470436148
Book Description
The automorphisms of a two-generator free group $mathsf F2$ acting on the space of orientation-preserving isometric actions of $mathsf F2$ 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) := -x2 -y2 + z2 + x y z -2 $ and an area form on the level surfaces $kappa Phi-1(k)$.
About the Author
The automorphisms of a two-generator free group $mathsf F2$ acting on the space of orientation-preserving isometric actions of $mathsf F2$ 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) := -x2 -y2 + z2 + x y z -2 $ and an area form on the level surfaces $kappa Phi-1(k)$. Read more