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The automorphism groups of the profinite braid groups

· 2019 · math.GT · arXiv 1904.06749

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abstract

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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math.GT 1

years

2020 1

verdicts

UNVERDICTED 1

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Automorphisms of profinite mapping class groups

math.GT · 2020-11-30 · 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)).

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  • Automorphisms of profinite mapping class groups math.GT · 2020-11-30 · unverdicted · none · ref 24 · internal anchor

    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)).