The first integral cohomology of pure mapping class groups
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866913257277620224 |
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| author | Aramayona, Javier Patel, Priyam Vlamis, Nicholas G. |
| author_facet | Aramayona, Javier Patel, Priyam Vlamis, Nicholas G. |
| contents | It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping class groups to the integers. Moreover, we compute the first integral cohomology group associated to the pure mapping class group of any connected orientable surface of genus at least 2 in terms of the surface's simplicial homology. In order to do this, we show that pure mapping class groups of infinite-genus surfaces split as a semi-direct product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_03132 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | The first integral cohomology of pure mapping class groups Aramayona, Javier Patel, Priyam Vlamis, Nicholas G. Geometric Topology Group Theory It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we construct nontrivial homomorphisms from infinite-genus mapping class groups to the integers. Moreover, we compute the first integral cohomology group associated to the pure mapping class group of any connected orientable surface of genus at least 2 in terms of the surface's simplicial homology. In order to do this, we show that pure mapping class groups of infinite-genus surfaces split as a semi-direct product. |
| title | The first integral cohomology of pure mapping class groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/1711.03132 |