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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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This content will become publicly available on January 5, 2026
Profinite properties of algebraically clean graphs of free groups
We prove that for every prime p algebraically clean graphs of groups are vir- tually residually p-finite and cohomologically p-complete. We also prove that they are cohomologically good. We apply this to certain 2-dimensional Artin groups.
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- Award ID(s):
- 2203325
- PAR ID:
- 10591172
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of pure and applied algebra
- ISSN:
- 0022-4049
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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