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Deforming convex
projective manifolds
Daryl Cooper, Darren Long and Stephan Tillmann |
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Geometry & Topology 22 (2018) 1349–1404
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Abstract |
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We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul, which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an open subset of the representation variety. We also give a relative version for noncompact manifolds of the openness of their holonomies. |
Keywords
projective structure, deformation, cusp, properly convex
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Mathematical Subject Classification 2010
Primary: 57N16
Secondary: 57M50
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References |
Publication
Received: 5 February 2016
Revised: 28 April 2017
Accepted: 14 July 2017
Published: 16 March 2018
Proposed: Benson Farb
Seconded: Ian Agol, Anna Wienhard
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Authors |
| Daryl Cooper | |
| Department of Mathematics University of California Santa Barbara, CA United States |
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| http://web.math.ucsb.edu/~cooper/ | |
| Darren Long | |
| Department of Mathematics University of California Santa Barbara, CA United States |
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| http://web.math.ucsb.edu/~long/ | |
| Stephan Tillmann | |
| School of Mathematics and
Statistics The University of Sydney Sydney, NSW Australia |
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| http://www.maths.usyd.edu.au/u/tillmann/ | |
