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Automorphisms of braid groups on orientable surfaces

Byung Hee An

Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea

https://doi.org/10.1142/S021821651650022XCited by:3 (Source: Crossref)

Abstract

In this paper, we compute the automorphism groups $Aut (P_{n} (Σ))$ and $Aut (B_{n} (Σ))$ of braid groups $P_{n} (Σ)$ and $B_{n} (Σ)$ on every orientable surface $Σ$ , which are isomorphic to group extensions of the extended mapping class group $ℳ_{n}^{*} (Σ)$ by the transvection subgroup except for a few cases. We also prove that $P_{n} (Σ)$ is always a characteristic subgroup of $B_{n} (Σ)$ , unless $Σ$ is a twice-punctured sphere and $n = 2$ .

Keywords:

AMSC: 20F36, 20F28, 32G15

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