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- W4297484022 abstract "Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for every such complete hyperbolic surface Sigma, the deformation space identifies with two opposite octants in R^3. Furthermore every M admits a fundamental polyhedron bounded by crooked planes. Therefore M 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 Sp(4,Z)." @default.
- W4297484022 created "2022-09-29" @default.
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- W4297484022 date "2009-07-03" @default.
- W4297484022 modified "2023-09-23" @default.
- W4297484022 title "Affine deformations of a three-holed sphere" @default.
- W4297484022 doi "https://doi.org/10.48550/arxiv.0907.0690" @default.
- W4297484022 hasPublicationYear "2009" @default.
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