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.
Authors
- Benjamin A. Appiah
- Wenchao Ge (ORCID: https://orcid.org/0000-0003-1936-7710)
- Sonal Jain (ORCID: https://orcid.org/0000-0002-4094-2575)
- Pallavi Dani (ORCID: https://orcid.org/0000-0001-7653-2618)
- Justin Murray
- Kevin Schreve (ORCID: https://orcid.org/0000-0002-3163-3404)
- Adithyan Pandikkadan
- Matthew Lemoine
- Charles E. Hudson
- Jake Murphy (ORCID: https://orcid.org/0009-0009-8423-0260)
- Huong Vo
Institutions
- Louisiana State University (US)
Publication Details
- Journal
- International Journal of Algebra and Computation
- Published
- 2024-10-18
- DOI
- https://doi.org/10.1142/s0218196724500528
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00