Homotopical presentations of braid groups via reduced lifts

James Tao; Roman Travkin

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arXiv · 2103.13543

Homotopical presentations of braid groups via reduced lifts

James Tao·Roman Travkin

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Abstract

In 1997, Deligne showed that the reduced lift presentation of a finite type generalized braid group remains correct if it is (suitably) interpreted as a presentation of a topological monoid. In this expository paper, we point out that Deligne's argument does not require the 'finite type' hypothesis, so it gives a different proof of a theorem proved by Dobrinskaya in 2006. We also review how to use this result to construct an action of the braid group on the finite or affine Hecke $\infty$-category via intertwining functors.

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James Tao, Roman Travkin. 2021-03-25. Homotopical presentations of braid groups via reduced lifts. https://arxiv.org/abs/2103.13543

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