Automatic continuity for homeomorphism groups and applications
Automatic continuity for homeomorphism groups and applications
复制标题
同胚群和应用的自动连续性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Kathryn Mann
中科院分区：
文献类型：
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作者：
Kathryn Mann
设M是一个紧流形，可能有边界.我们证明了M的同胚群具有自动连续性：从Homeo（M）到任何可分群的任何同态必连续。这回答了C的一个问题。罗森达尔如果N是M的子流形，则M的保持N的同胚群也具有此性质。自动连续性的各种应用进行了讨论，包括应用到拓扑和结构群的芽同胚。在附录中与弗雷德里克勒鲁我们还表明，使用相关的技术，该组芽在一个点的同胚的Rn是强一致简单的。
Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property: any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a question of C. Rosendal. If N is a submanifold of M, the group of homeomorphisms of M that preserve N also has this property. Various applications of automatic continuity are discussed, including applications to the topology and structure of groups of germs of homeomorphisms. In an appendix with Frederic Le Roux we also show, using related techniques, that the group of germs at a point of homeomorphisms of Rn is strongly uniformly simple.