Geodesic
The $K(\pi,1)$ problem for the affine Artin group of type $\widetilde{B}_n$ and its cohomology
Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 1-22 Cet article a éte moissonné depuis la source EMS Press

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We prove that the complement to the affine complex arrangement of type Bn​ is a K(π,1) space. We also compute the cohomology of the affine Artin group GBn​​ (of type Bn​) with coefficients in interesting local systems. In particular, we consider the module Q[q±1,t±1], where the first n standard generators of GBn​​ act by (−q)-multiplication while the last generator acts by (−t) multiplication. Such a representation generalizes the analogous 1-parameter representation related to the bundle structure over the complement to the discriminant hypersurface, endowed with the monodromy action of the associated Milnor fibre. The cohomology of GBn​​ with trivial coefficients is derived from the previous one.
DOI : 10.4171/jems/187
Classification : 20-XX, 00-XX
Keywords: Affine Artin groups, twisted cohomology, group representations 
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     title = {The $K(\pi,1)$ problem for the affine {Artin} group of type $\widetilde{B}_n$ and its cohomology},
     journal = {Journal of the European Mathematical Society},
     pages = {1--22},
     year = {2010},
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     doi = {10.4171/jems/187},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/187/}
}
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Filippo Callegaro; Davide Moroni; Mario Salvetti. The $K(\pi,1)$ problem for the affine Artin group of type $\widetilde{B}_n$ and its cohomology. Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 1-22. doi: 10.4171/jems/187

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