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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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Characterizing candidates for Cannon's conjecture from geometric measure theory
Abstract We show that recent work of Song implies that torsion‐free hyperbolic groups with Gromov boundary arerealized as fundamental groups of closed 3‐manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3‐manifold, and suggest some related questions.
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- PAR ID:
- 10397822
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Bulletin of the London Mathematical Society
- Volume:
- 55
- Issue:
- 4
- ISSN:
- 0024-6093
- Page Range / eLocation ID:
- p. 1718-1725
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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