Volume 22, issue 3 (2018)

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Deforming convex projective manifolds

Daryl Cooper, Darren Long and Stephan Tillmann

Geometry & Topology 22 (2018) 1349–1404

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.

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projective structure, deformation, cusp, properly convex
Mathematical Subject Classification 2010
Primary: 57N16
Secondary: 57M50
Received: 5 February 2016
Revised: 28 April 2017
Accepted: 14 July 2017
Published: 16 March 2018
Proposed: Benson Farb
Seconded: Ian Agol, Anna Wienhard
Daryl Cooper
Department of Mathematics
University of California
Santa Barbara, CA
United States
Darren Long
Department of Mathematics
University of California
Santa Barbara, CA
United States
Stephan Tillmann
School of Mathematics and Statistics
The University of Sydney
Sydney, NSW