The <em>K</em>(<em>π</em>,1) problem for the affine Artin group of type <span style="text-decoration: overline;"><em>B</em></span><sub><em>n</em></sub> and its cohomology
Mario Salvetti
Università di Pisa, ItalyFilippo Callegaro
Scuola Normale Superiore, Pisa, ItalyDavide Moroni
National Research Council of Italy (CNR), Pisa, Italy

Abstract
We prove that the complement to the affine complex arrangement of type B__n is a K(π,1) space. We also compute the cohomology of the affine Artin group G__B__n (of type B__n) with coefficients in interesting local systems. In particular, we consider the module ℚ[q_±1 , t_±1], where the first n standard generators of G__B__n 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 G__B__n with trivial coefficients is derived from the previous one.
Cite this article
Mario Salvetti, Filippo Callegaro, Davide Moroni, The <em>K</em>(<em>π</em>,1) problem for the affine Artin group of type <span style="text-decoration: overline;"><em>B</em></span><sub><em>n</em></sub> and its cohomology. J. Eur. Math. Soc. 12 (2010), no. 1, pp. 1–22
DOI 10.4171/JEMS/187