On properly convex real-projective manifolds with Generalized Cusp

Abstract

Suppose $E$ is an end of an irreducible, properly convex, real-projective $n$-manifold $M$. If ${\pi }_{1}E$ contains a subgroup of finite index isomorphic to ${\mathbb{Z}}^{n-1}$, and $E\hookrightarrow M$ is ${\pi }_1$-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.

References in corpus (1)

• The classification of ends of properly convex real projective orbifolds II: Properly convex radial ends and totally geodesic ends

Cited by in corpus (1)

• The space of properly-convex structures