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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.04422 |
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Table of 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.