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arXiv · 1708.08383

Isomorphisms between big mapping class groups

Juliette Bavard·Spencer Dowdall·Kasra Rafi
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Abstract

We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these `big' mapping class groups and shows that each finite-index subgroup has finite outer automorphism group. As a key ingredient, we prove that all simplicial automorphisms between curve complexes of infinite-type orientable surfaces are induced by homeomorphisms.

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Juliette Bavard, Spencer Dowdall, Kasra Rafi. 2017-08-28. Isomorphisms between big mapping class groups. https://arxiv.org/abs/1708.08383

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