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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Bibliographic Details
Published in:Transformation groups 2016-12, Vol.21 (4), p.953-1002
Main Authors: CHARETTE, VIRGINIE, DRUMM, TODD A., GOLDMAN, WILLIAM M.
Format: Article
Language:English
Subjects:
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Polyhedra
Topological Groups
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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