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Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane (Paperback)
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Automorphisms of Two-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane (Paperback)
Series: Memoirs of the American Mathematical Society
Expected to ship within 12 - 17 working days
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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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