Homotopy braid groups are torsion-free

Emmanuel Graff

doi:10.1093/imrn/rnaf275

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arXiv · 2405.04422

Homotopy braid groups are torsion-free

Emmanuel Graff

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Abstract

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.

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Emmanuel Graff. 2024-05-07. Homotopy braid groups are torsion-free. https://doi.org/10.1093/imrn%2Frnaf275

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