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Surjective homomorphisms between surface braid groups

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Abstract

Let PBn(Sg,p) be the pure braid group of a genus g > 1 surface with p punctures. In this paper we prove that any surjective homomorphism PBn(Sg,p) → PBm(Sg,p) factors through one of the forgetful homomorphisms. We then compute the automorphism group of PBm(Sg,p), which gives a simpler proof of Irmak–Ivanov–McCarthy [IIM03, Theorem 1]. Surprisingly, in contrast to the n = 1 case, any automorphism of PBn(Sg,p) for n > 1 is geometric.

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Authors and Affiliations

  1. The Division of Physics, Mathematics and Astronomy, California Institute of Technology, 1200 E California Blvd, Pasadena, CA, 91125, USA

    Lei Chen

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  1. Lei Chen
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Chen, L. Surjective homomorphisms between surface braid groups. Isr. J. Math. 232, 483–500 (2019). https://doi.org/10.1007/s11856-019-1881-7

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  • DOI: https://doi.org/10.1007/s11856-019-1881-7

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