Convex co-compact representations of 3-manifold groups

2020/09/11 by Islam, Mitul, Zimmer, Andrew
#20F67 #20H10 #53A20 #53A35 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2009.05191

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 × Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples.

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