Homotopy braid groups are torsion-free
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911870015766528 |
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| author | Graff, Emmanuel |
| author_facet | Graff, Emmanuel |
| contents | We show that, for any number of components, the group of braids up to link-homotopy is torsion-free. This generalizes a result of Humphries up to six components, and provides an explicit solution to a question posed by Lin and addressed by Linell and Schick regarding the existence of non-abelian torsion-free quotients of the braid group. The proof relies on the diagrammatic theory of welded braids and uses the Artin representation. As a corollary, we obtain yet another proof that braid groups themselves are torsion-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy braid groups are torsion-free Graff, Emmanuel Geometric Topology We show that, for any number of components, the group of braids up to link-homotopy is torsion-free. This generalizes a result of Humphries up to six components, and provides an explicit solution to a question posed by Lin and addressed by Linell and Schick regarding the existence of non-abelian torsion-free quotients of the braid group. The proof relies on the diagrammatic theory of welded braids and uses the Artin representation. As a corollary, we obtain yet another proof that braid groups themselves are torsion-free. |
| title | Homotopy braid groups are torsion-free |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2405.04422 |