Mathematics > Algebraic Topology
[Submitted on 25 Jul 2022 (v1), last revised 19 Feb 2024 (this version, v2)]
Title:Fox-Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups
View PDFAbstract:In this paper, we will develop a family of braid representations of Artin groups of type B from braided vector spaces, and identify the homology of these groups with these coefficients with the cohomology of a specific bimodule over a quantum shuffle algebra. As an application, we give a complete characterization of the homology of type-B Artin groups with coefficients in one-dimensional braid representations over a field of characteristic 0. We will also discuss two different approaches to this computation: the first method extends a computation of the homology of braid groups due to Ellenberg-Tran-Westerland by means of induced representation, while the second method involves constructing a cellular stratification for configuration spaces of the punctured complex plane.
Submission history
From: Anh Trong Nam Hoang [view email][v1] Mon, 25 Jul 2022 18:41:02 UTC (42 KB)
[v2] Mon, 19 Feb 2024 04:41:26 UTC (44 KB)
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