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Nielsen realization problem : ウィキペディア英語版 | Nielsen realization problem The Nielsen realization problem is a question asked by about whether finite subgroups of mapping class groups can act on surfaces, that was answered positively by . ==Statement== Given an oriented surface, we can divide the group Diff(''S''), the group of diffeomorphisms of the surface to itself, into isotopy classes to get the mapping class group π0(Diff(''S'')). The conjecture asks whether a finite subgroup of the mapping class group of a surface can be realized as the isometry group of a hyperbolic metric on the surface. The mapping class group acts on Teichmüller space. An equivalent way of stating the question asks whether every finite subgroup of the mapping class group fixes some point of Teichmüller space.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Nielsen realization problem」の詳細全文を読む
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