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• W3088894305 abstract "Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 1983, Kerckhoff showed that for S a finite-type surface, any finite subgroup G may be realized as a group of isometries of some hyperbolic metric on S. We extend Kerckhoff's result to orientable, infinite-type surfaces. As applications, we classify torsion elements in the mapping class group of the plane minus a Cantor set, and also show that topological groups containing sequences of torsion elements limiting to the identity do not embed continuously into the mapping class group of S. Finally, we show that compact subgroups of the mapping class group of S are finite, and locally compact subgroups are discrete." @default.
• W3088894305 created "2020-10-01" @default.
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• W3088894305 date "2021-01-26" @default.
• W3088894305 modified "2023-09-27" @default.
• W3088894305 title "Nielsen realization for infinite-type surfaces" @default.
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• W3088894305 doi "https://doi.org/10.1090/proc/15316" @default.
• W3088894305 hasPublicationYear "2021" @default.
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