Some topological problems on the configuration spaces of Artin and Coxeter groups
Abstract
In the first part we review some topological and algebraic aspects in the theory of Artin and Coxeter groups, both in the finite and infinite case (but still, finitely generated). In the following parts, among other things, we compute the Schwartz genus of the covering associated to the orbit space for all affine Artin groups. We also give a partial computation of the cohomology of the braid group with non-abelian coefficients coming from geometric representations. We introduce an interesting class of "sheaves over posets", which we call "weighted sheaves over posets", and use them for explicit computations.
Keywords
Cite
@article{arxiv.1404.2594,
title = {Some topological problems on the configuration spaces of Artin and Coxeter groups},
author = {D. Moroni and M. Salvetti and A. Villa},
journal= {arXiv preprint arXiv:1404.2594},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1404.2392. Proceedings of Configuration spaces: geometry, combinatorics and topology, CRM E.De Giorgi, 2010, Edizioni della Scuola Normale Superiore