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 $kappa Phi-1(k)$.

未经允许不得转载：Wow! eBook » Automorphisms of Two-generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane (Memoirs of the American Mathematical Society)