Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane

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) := -x^{2} -y^{2} + z^{2} + x y z -2 $ and an area form on the level surfaces $\kappa {\Phi}^{-1}(k)$.

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.