Convex co-compact representations of 3-manifold groups

Abstract

A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean $\times$ Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples.

v2: substantial changes from v1. Final version, to appear in the Journal of Topology. 48 pages. Comments welcome

References in corpus (5)

• Topological restrictions on Anosov representations
• Convex co-compact actions of relatively hyperbolic groups
• Relatively dominated representations
• Centralizers in 3-manifold groups
• Regularity of limit sets of Anosov representations