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Affine deformations of a
three-holed sphere
Virginie Charette, Todd A Drumm and William M Goldman |
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Geometry & Topology 14 (2010) 1355–1382
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Abstract |
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Associated to every complete affine 3–manifold with nonsolvable fundamental group is a noncompact hyperbolic surface . We classify these complete affine structures when is homeomorphic to a three-holed sphere. In particular, for every such complete hyperbolic surface , the deformation space identifies with two opposite octants in . Furthermore every admits a fundamental polyhedron bounded by crooked planes. Therefore is homeomorphic to an open solid handlebody of genus two. As an explicit application of this theory, we construct proper affine deformations of an arithmetic Fuchsian group inside . |
Keywords
hyperbolic surface, affine manifold, discrete group,
fundamental polygon, fundamental polyhedron, proper action,
Lorentz metric, Fricke space
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Mathematical Subject Classification 2000
Primary: 57M05
Secondary: 20H10, 30F60
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References |
Publication
Received: 7 October 2009
Revised: 10 May 2010
Accepted: 23 April 2010
Published: 4 June 2010
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, Benson Farb
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Authors |
| Virginie Charette | |
| Département de mathématiques Université de Sherbrooke Sherbrooke Québec J1K 2R1 Canada |
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| Todd A Drumm | |
| Department of Mathematics Howard University Washington DC 20059 USA |
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| William M Goldman | |
| Department of Mathematics University of Maryland College Park MD 20742 USA |
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