Asymptotic and cohomological dimension of surface braid groups and poly-surface groups
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| Format: | Preprint |
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2025
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| _version_ | 1866915966400593920 |
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| author | Álvarez, Porfirio L. León Morales, Israel |
| author_facet | Álvarez, Porfirio L. León Morales, Israel |
| contents | In this paper, we determine the asymptotic dimension for all surface braid groups -- including those associated with non-orientable and infinite-type surfaces -- as well as for torsion-free poly-finitely generated surface groups. We demonstrate that for both classes, the virtual cohomological dimension and the asymptotic dimension coincide. For poly-finitely generated surface groups and braid groups of finite-type surfaces, our approach establishes that these groups are virtual duality groups in the sense of Bieri-Eckmann. In the case of infinite-type surfaces, the argument is based on the fact that their braid groups are countable and normally poly-free. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_10706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic and cohomological dimension of surface braid groups and poly-surface groups Álvarez, Porfirio L. León Morales, Israel Group Theory Algebraic Topology 20F69, 20F65, 57M07 In this paper, we determine the asymptotic dimension for all surface braid groups -- including those associated with non-orientable and infinite-type surfaces -- as well as for torsion-free poly-finitely generated surface groups. We demonstrate that for both classes, the virtual cohomological dimension and the asymptotic dimension coincide. For poly-finitely generated surface groups and braid groups of finite-type surfaces, our approach establishes that these groups are virtual duality groups in the sense of Bieri-Eckmann. In the case of infinite-type surfaces, the argument is based on the fact that their braid groups are countable and normally poly-free. |
| title | Asymptotic and cohomological dimension of surface braid groups and poly-surface groups |
| topic | Group Theory Algebraic Topology 20F69, 20F65, 57M07 |
| url | https://arxiv.org/abs/2506.10706 |