Higher dimensional divergence for mapping class groups
In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures...
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| Format: | Journal article |
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European Mathematical Society
2019
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| _version_ | 1797064805526274048 |
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| author | Behrstock, J Drutu, C |
| author_facet | Behrstock, J Drutu, C |
| author_sort | Behrstock, J |
| collection | OXFORD |
| description | In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures minus 3). We also provide inductive constructions of CAT(0)--spaces with co-compact group actions, for which the divergence below the rank is (exactly) a polynomial function of our choice, with degree arbitrarily large compared to the dimension. |
| first_indexed | 2024-03-06T21:19:37Z |
| format | Journal article |
| id | oxford-uuid:40fe86e1-477f-4630-beb5-ede69ea1705e |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:19:37Z |
| publishDate | 2019 |
| publisher | European Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:40fe86e1-477f-4630-beb5-ede69ea1705e2022-03-26T14:41:04ZHigher dimensional divergence for mapping class groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:40fe86e1-477f-4630-beb5-ede69ea1705eSymplectic Elements at OxfordEuropean Mathematical Society2019Behrstock, JDrutu, CIn this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures minus 3). We also provide inductive constructions of CAT(0)--spaces with co-compact group actions, for which the divergence below the rank is (exactly) a polynomial function of our choice, with degree arbitrarily large compared to the dimension. |
| spellingShingle | Behrstock, J Drutu, C Higher dimensional divergence for mapping class groups |
| title | Higher dimensional divergence for mapping class groups |
| title_full | Higher dimensional divergence for mapping class groups |
| title_fullStr | Higher dimensional divergence for mapping class groups |
| title_full_unstemmed | Higher dimensional divergence for mapping class groups |
| title_short | Higher dimensional divergence for mapping class groups |
| title_sort | higher dimensional divergence for mapping class groups |
| work_keys_str_mv | AT behrstockj higherdimensionaldivergenceformappingclassgroups AT drutuc higherdimensionaldivergenceformappingclassgroups |