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Article Dans Une Revue International Mathematics Research Notices Année : 2020

Isomorphisms between big mapping class groups

Résumé

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.

Dates et versions

hal-02373851 , version 1 (21-11-2019)

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Juliette Bavard, Spencer Dowdall, Kasra Rafi. Isomorphisms between big mapping class groups. International Mathematics Research Notices, 2020, 10 (10), pp.3084-3099. ⟨10.1093/imrn/rny093⟩. ⟨hal-02373851⟩
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