The algebraic structure of hyperbolic graph braid groups
Group Theory
2024-03-22 v2 Geometric Topology
Abstract
Genevois recently classified which graph braid groups on strands are word hyperbolic. In the -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 -strand braid groups of sun graphs are free. On the other hand, it was known to experts that -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.
Keywords
Cite
@article{arxiv.2403.08623,
title = {The algebraic structure of hyperbolic graph braid groups},
author = {B. Appiah and P. Dani and W. Ge and C. Hudson and S. Jain and M. Lemoine and J. Murphy and J. Murray and A. Pandikkadan and K. Schreve and H. Vo},
journal= {arXiv preprint arXiv:2403.08623},
year = {2024}
}
Comments
Based on work from a Louisiana State University VIR (Vertically Integrated Research) course. In v2, we reworded the introduction to better reflect what was previously known in the pulsar case and corrected some typos