The algebraic structure of hyperbolic graph braid groups

Authors

Benjamin Appiah, Louisiana State University
Pallavi Dani, Louisiana State University
Wayne Ge, Louisiana State University
Christopher Hudson, Louisiana State University
Saumya Jain, Louisiana State University
Matthew Lemoine, Louisiana State University
Jake Murphy, Louisiana State University
Justin Murray, Louisiana State University
Adithyan Pandikkadan, Louisiana State University
Kevin Schreve, Louisiana State University
Huong Vo, Louisiana State University

Document Type

Article

Publication Date

5-1-2025

Abstract

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.

Publication Source (Journal or Book title)

International Journal of Algebra and Computation

First Page

329

Last Page

342

Recommended Citation

Appiah, B., Dani, P., Ge, W., Hudson, C., Jain, S., Lemoine, M., Murphy, J., Murray, J., Pandikkadan, A., Schreve, K., & Vo, H. (2025). The algebraic structure of hyperbolic graph braid groups. International Journal of Algebra and Computation, 35 (3), 329-342. https://doi.org/10.1142/S0218196724500528