Semisimple actions of mapping class groups on CAT(0) spaces
Let Σ be an orientable surface of finite type and let Mod(Σ) be its mapping class group. We consider actions of Mod(Σ) by semisimple isometries on complete CAT(0) spaces. If the genus of Σ is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(Σ) on the...
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| Format: | Book section |
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Cambridge University Press
2013
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| _version_ | 1797058014678614016 |
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| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | Let Σ be an orientable surface of finite type and let Mod(Σ) be its mapping class group. We consider actions of Mod(Σ) by semisimple isometries on complete CAT(0) spaces. If the genus of Σ is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(Σ) on the completion of Teichmüller 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. |
| first_indexed | 2024-03-06T19:44:37Z |
| format | Book section |
| id | oxford-uuid:21d7c251-5d8c-4882-bca0-53b95ebb3acb |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:44:37Z |
| publishDate | 2013 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:21d7c251-5d8c-4882-bca0-53b95ebb3acb2022-03-26T11:35:36ZSemisimple actions of mapping class groups on CAT(0) spacesBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:21d7c251-5d8c-4882-bca0-53b95ebb3acbSymplectic Elements at OxfordCambridge University Press2013Bridson, MLet Σ be an orientable surface of finite type and let Mod(Σ) be its mapping class group. We consider actions of Mod(Σ) by semisimple isometries on complete CAT(0) spaces. If the genus of Σ is at least 3, then in any such action all Dehn twists act as elliptic isometries. The action of Mod(Σ) on the completion of Teichmüller 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. |
| spellingShingle | Bridson, M Semisimple actions of mapping class groups on CAT(0) spaces |
| title | Semisimple actions of mapping class groups on CAT(0) spaces |
| title_full | Semisimple actions of mapping class groups on CAT(0) spaces |
| title_fullStr | Semisimple actions of mapping class groups on CAT(0) spaces |
| title_full_unstemmed | Semisimple actions of mapping class groups on CAT(0) spaces |
| title_short | Semisimple actions of mapping class groups on CAT(0) spaces |
| title_sort | semisimple actions of mapping class groups on cat 0 spaces |
| work_keys_str_mv | AT bridsonm semisimpleactionsofmappingclassgroupsoncat0spaces |