Semisimple actions of mapping class groups on CAT(0) spaces
Semisimple actions of mapping class groups on CAT(0) spaces
复制标题
将类组映射到 CAT(0) 空间的半简单操作
DOI：
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发表时间：
2009
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通讯作者：
M. Bridson
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文献类型：
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作者：
M. Bridson
设S为有限型的可定向曲面，设Mod(S)为其映射类群。在完全CAT(0)空间上用半简单等距考虑Mod(S)的作用。如果S的属至少为3，那么在任何这样的作用下，所有Dehn扭转都表现为椭圆等距。Mod(S)对Weil-Petersson度规补全Teichm ' uller空间的作用表明存在这类有趣的作用。
Let S be an orientable surface of finite type and let Mod(S) be its mapping class group. We consider actions of Mod(S) by semisimple isometries on complete CAT(0) spaces. If the genus of S is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(S) on the completion of Teichm"uller space with the Weil-Petersson metric shows that there are interesting actions of this type.
Whenever the mapping class group of a closed orientable surface of genus g acts by semisimple isometries on a complete CAT(0) space of dimension less than g it must fix a point.
The mapping class group of a closed surface of genus 2 acts properly by semisimple isometries on a complete CAT(0) space of dimension 18.