Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane, Paperback / softback Book

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

Part of the Memoirs of the American Mathematical Society series

Paperback / softback

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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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