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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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Largest hyperbolic action of 3‐manifold groups
Abstract The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. Following Abbott–Balasubramanya–Osin, the group is ‐accessibleif the resulting poset has a largest element. In this paper, we prove that every nongeometric 3‐manifold has a finite cover with ‐inaccessible fundamental group and give conditions under which the fundamental group of the original manifold is ‐inaccessible. We also prove that every Croke–Kleiner admissible group (a class of graphs of groups that generalizes fundamental groups of three‐dimensional graph manifolds) has a finite index subgroup that is ‐inaccessible.
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- PAR ID:
- 10598332
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 56
- Issue:
- 10
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- 3090 to 3113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1112/blms.13118
