The proper geometric dimension of the mapping class group of an orientable surface with punctures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910752297713664 |
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| author | Colin, Nestor Rolland, Rita Jiménez Álvarez, Porfirio L. León Saldaña, Luis Jorge Sánchez |
| author_facet | Colin, Nestor Rolland, Rita Jiménez Álvarez, Porfirio L. León Saldaña, Luis Jorge Sánchez |
| contents | We show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed orientable surfaces and for {\it pure} mapping class groups by Aramayona and Martínez Pérez.
As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The proper geometric dimension of the mapping class group of an orientable surface with punctures Colin, Nestor Rolland, Rita Jiménez Álvarez, Porfirio L. León Saldaña, Luis Jorge Sánchez Geometric Topology Group Theory We show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed orientable surfaces and for {\it pure} mapping class groups by Aramayona and Martínez Pérez. As a consequence of our result we also obtain the proper geometric dimension of {\it full} spherical braid groups. |
| title | The proper geometric dimension of the mapping class group of an orientable surface with punctures |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2412.14410 |