Deforming convex projective manifolds

Cooper, Daryl¹ ; Long, Darren¹ ; Tillmann, Stephan²

¹ Department of Mathematics, University of California, Santa Barbara, CA, United States
² School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, Australia

Geometry & topology, Tome 22 (2018) no. 3, pp. 1349-1404

Résumé

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.

Détail

DOI : 10.2140/gt.2018.22.1349

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

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