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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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Islam et al. (Wed,) studied this question.
www.synapsesocial.com/papers/68e6c32cb6db643587641f20 — DOI: https://doi.org/10.1112/topo.12332
Mitul Islam
Andrew Zimmer
Journal of Topology
University of Michigan
University of Wisconsin–Madison
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