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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… Click to show full 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.
Keywords:
surjective homomorphisms;
homomorphisms surface;
surface;
surface braid;
braid groups
Journal Title: Israel Journal of Mathematics
Year Published: 2019
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Journal Title: Israel Journal of Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!