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Deforming convex projective manifolds

Daryl Cooper, Darren Long and Stephan Tillmann

Geometry & Topology 22 (2018) 1349–1404
Abstract

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 (G,X) manifolds of the openness of their holonomies.

Keywords
projective structure, deformation, cusp, properly convex
Mathematical Subject Classification 2010
Primary: 57N16
Secondary: 57M50
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
Authors
Daryl Cooper
Department of Mathematics
University of California
Santa Barbara, CA
United States
http://web.math.ucsb.edu/~cooper/
Darren Long
Department of Mathematics
University of California
Santa Barbara, CA
United States
http://web.math.ucsb.edu/~long/
Stephan Tillmann
School of Mathematics and Statistics
The University of Sydney
Sydney, NSW
Australia
http://www.maths.usyd.edu.au/u/tillmann/