On properly convex real-projective manifolds with Generalized Cusp

2020/09/14 by Daryl Cooper, Stephan Tillmann, Cooper, Daryl +1
Mathematics · #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.2009.06569

arxiv created 2020/09/14 · arxiv updated 2020/09/15

Abstract

Suppose E is an end of an irreducible, properly convex, real-projective n-manifold M. If π₁E contains a subgroup of finite index isomorphic to \mathbb Z^n-1, and E\hookrightarrow M is π₁-injective, then E is a generalized cusp. We list some consequences when all ends are of this type. Under certain hypotheses we prove the holonomy of a properly convex manifold is irreducible.

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