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 strands to the pure mapping class group of a nonoriantable surface of genus . For and 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.
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