Geometric representations of the braid group on a nonorientable surface

Abstract

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