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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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This content will become publicly available on May 1, 2026
The algebraic structure of hyperbolic graph braid groups
Genevois recently classified which graph braid groups are word hyperbolic. In the 3-strand case, he asked whether all such word hyperbolic groups are actually free; this reduced to checking two infinite classes of graphs: sun and pulsar graphs. We prove that 3-strand braid groups of sun graphs are free. On the other hand, it was known to experts that 3-strand braid groups of most pulsar graphs contain surface subgroups. We provide a simple proof of this and prove an additional structure theorem for these groups.
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- PAR ID:
- 10591175
- Publisher / Repository:
- World Scientific Connect
- Date Published:
- Journal Name:
- International Journal of Algebra and Computation
- Volume:
- 35
- Issue:
- 03
- ISSN:
- 0218-1967
- Page Range / eLocation ID:
- 329 to 342
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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