A generalization of the Epstein-Penner construction to projective manifolds

2013/07/18 by Daryl Cooper, D. D. Long, Cooper, Daryl +2
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematics and Applications #Point processes and geometric inequalities #math.GT

paper · pdf · doi:10.48550/arxiv.1307.5016

8 pages, 1 figure

arxiv created 2013/07/18 · openalex publication_date 2013/07/18 · arxiv updated 2013/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the canonical cell decomposition due to Epstein and Penner of a hyperbolic manifold with cusps to the strictly convex setting. It follows that a sufficiently small deformation of the holonomy of a finite volume strictly convex real projective manifold is the holonomy of some nearby projective structure with radial ends, provided the holonomy of each cusp has a fixed point.

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