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
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 $\left(G,X\right)$ manifolds of the openness of their holonomies.

Keywords
projective structure, deformation, cusp, properly convex
Primary: 57N16
Secondary: 57M50