English

Geometric representations of the braid group on a nonorientable surface

Geometric Topology 2025-07-18 v2

Abstract

We classify homomorphisms from the braid group on nn strands to the pure mapping class group of a nonoriantable surface of genus gg. For n14n\ge 14 and g2n/2+1g\le 2\lfloor{n/2}\rfloor+1 every such homomorphism is either cyclic, or it maps standard generators of the braid group to either distinct Dehn twists, or distinct crosscap transpositions, possibly multiplied by the same element of the centralizer of the image.

Keywords

Cite

@article{arxiv.2408.04707,
  title  = {Geometric representations of the braid group on a nonorientable surface},
  author = {Michał Stukow and Błażej Szepietowski},
  journal= {arXiv preprint arXiv:2408.04707},
  year   = {2025}
}

Comments

Minor edits and updated comparison with the case of an orientable surface

R2 v1 2026-06-28T18:08:06.137Z