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arxiv: 1904.06749 · v2 · pith:STM6PHEFnew · submitted 2019-04-14 · 🧮 math.GT · math.GR

The automorphism groups of the profinite braid groups

Arata Minamide , Hiroaki Nakamura This is my paper
classification 🧮 math.GT math.GR
keywords groupsprofiniteautomorphismbraiddeterminefourgrothendieck-teichmgroup
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In this paper we determine the automorphism groups of the profinite braid groups with four or more strings in terms of the profinite Grothendieck-Teichm\"uller group.

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  1. Automorphisms of profinite mapping class groups

    math.GT 2020-11 unverdicted novelty 7.0

    For surfaces S with χ(S)<g-2 and (g,n)≠(1,2), Out^{I_0}(P check Γ(S)) is naturally isomorphic to Σ_n × hat{GT}, with a faithful embedding of hat{GT} into Out^{I_0}(P hat Γ(S)).