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arXiv · 2308.01410

Fox-Neuwirth cells, quantum shuffle algebras, and character sums of the resultant

Anh Trong Nam Hoang
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Abstract

We give an upper bound on character sums of the resultant over pairs of monic square-free polynomials of given degrees, answering a question of Ellenberg and Shusterman in the quadratic case. Our approach is topological: we compute the homology of braid groups on multi-punctured planes and prove a vanishing range for the homology of mixed braid groups with rank-1 local coefficients associated to characters of finite fields. Our method involves constructing a cellular stratification for configuration spaces of multi-punctured planes and relating their twisted homology with more general exponential coefficients to the cohomology of certain bimodules over quantum shuffle algebras.

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BibTeXRIS

Anh Trong Nam Hoang. 2023-08-02. Fox-Neuwirth cells, quantum shuffle algebras, and character sums of the resultant. https://arxiv.org/abs/2308.01410

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