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

Name: Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
Author: William Goldman

William Goldman

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ca. 121,50 €

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American Mathematical Society

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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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