PROPER AFFINE DEFORMATIONS OF THE ONE-HOLED TORUS

A Margulis spacetime is a complete at Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface ∑ homotopy-equivalent to M . The purpose of this paper is to classify Margulis spacetimes when ∑ is homeomorphic to a one-holed torus. We show that e...

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Published inTransformation groups Vol. 21; no. 4; pp. 953 - 1002
Main Authors CHARETTE, VIRGINIE, DRUMM, TODD A., GOLDMAN, WILLIAM M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2016
Springer Nature B.V
Subjects
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
Toruses
Triangles
Triangulation
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Summary:A Margulis spacetime is a complete at Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface ∑ homotopy-equivalent to M . The purpose of this paper is to classify Margulis spacetimes when ∑ is homeomorphic to a one-holed torus. We show that every such M decomposes into polyhedra bounded by crooked planes, corresponding to an ideal triangulation of ∑. This paper classifies and analyzes the structure of crooked ideal triangles , which play the same role for Margulis spacetimes as ideal triangles play for hyperbolic surfaces.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-016-9413-6