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Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
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Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
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eBook
Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane
2019
Overview
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).
Publisher
American Mathematical Society
Subject
ISBN
1470436140, 9781470436148
