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arXiv · 2408.04707

Geometric representations of the braid group on a nonorientable surface

Michał Stukow·Błażej Szepietowski
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Abstract

We classify homomorphisms from the braid group on $n$ strands to the pure mapping class group of a nonoriantable surface of genus $g$. For $n\ge 14$ and $g\le 2\lfloor{n/2}\rfloor+1$ 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.

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Michał Stukow, Błażej Szepietowski. 2025-07-16. Geometric representations of the braid group on a nonorientable surface. https://arxiv.org/abs/2408.04707

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