Surjective homomorphisms between surface braid groups

Lei Chen

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arXiv · 1704.05142

Surjective homomorphisms between surface braid groups

Lei Chen

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Abstract

Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then compute the automorphism group of $PB_n(S_{g,p})$, extending Irmak, Ivanov and McCarthy's result to the punctured case. Surprisingly, in contrast to the $n=1$ case, any automorphism of $PB_n(S_{g,p})$, $n>1$ is geometric.

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BibTeX RIS

Lei Chen. 2017-04-17. Surjective homomorphisms between surface braid groups. https://arxiv.org/abs/1704.05142

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