Isomorphisms Between Big Mapping Class Groups
Isomorphisms Between Big Mapping Class Groups
复制标题
大映射类组之间的同构
DOI：
10.1093/imrn/rny093
复制
发表时间：
2018
影响因子：
1
通讯作者：
Rafi, Kasra
中科院分区：
文献类型：
--
作者：
Bavard, Juliette;Dowdall, Spencer;Rafi, Kasra
我们证明了可定向无限型曲面的映射类群之间的任何同构都是由曲面之间的同胚引起的。我们的论点还适用于这些“大”映射类群的有限指数子群之间的自同构，并表明每个有限指数子群有有限的外自同构群。作为一个关键的成分，我们证明了所有的单纯自同构之间的曲线复合的无限型定向曲面的同胚诱导。
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.