Cohomology of affine Artin groups and applications
| dc.creator | Callegaro, Filippo | |
| dc.creator | Moroni, Davide | |
| dc.creator | Salvetti, Mario | |
| dc.date | 2007-05-19 | |
| dc.date.accessioned | 2026-07-07T08:02:32Z | |
| dc.date.available | 2026-07-07T08:02:32Z | |
| dc.description | The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type B_n with coefficients over the module \Q[q^{\pm 1},t^{\pm 1}]. Here the first (n-1) standard generators of the group act by (-q)-multiplication, while the last one acts by (-t)-multiplication. The proof uses some technical results from previous papers plus computations over a suitable spectral sequence. The remaining cases follow from an application of Shapiro's lemma, by considering some well-known inclusions: we obtain the rational cohomology of the Artin group of affine type \tilde{A}_{n} as well as the cohomology of the classical braid group {Br}_{n} with coefficients in the n-dimensional representation presented in \cite{tong}. The topological counterpart is the explicit construction of finite CW-complexes endowed with a free action of the Artin groups, which are known to be K(π,1) spaces in some cases (including finite type groups). Particularly simple formulas for the Euler-characteristic of these orbit spaces are derived. | |
| dc.description | 21 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0705.2823 | |
| dc.identifier | http://arxiv.org/abs/0705.2823 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129256 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 20J06; 20F36 | |
| dc.title | Cohomology of affine Artin groups and applications | |
| dc.type | text |