Automorphisms of two-generator free groups and spaces of isometric actions on the hyperbolic plane
| Autor: | Goldman, William, McShane, Greg, Stantchev, George, Tan, Ser Peow |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of 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 on R^3 by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces. We describe the dynamical decomposition of this action. The domain of discontinuity of this action corresponds to geometric structures: either complete hyperbolic structures on the 2-holed cross-surface (projective plane) with cusps and funnels, or complete hyperbolic structures on a one-holed Klein bottle, or hyperbolic structures on a Klein bottle with one conical singularity. The action is ergodic on the complement of the orbit of the Fricke space of the 2-holed cross-surface, and we show that the orbit of the generalized Fricke space of the one-holed Klein bottle is open and dense. Comment: 82 pages, 12 figures. This paper superceds and greatly expands our previous submission math.GT.0309072v1. The second revision corrects several errors, improves exposition and adds a new section. The third version incorporates comments of the referee. The paper will appear in Memoirs of the American Mathematical Society |
| Databáze: | arXiv |
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