The K(π, 1) problem for the affine Artin group of type \widetilde{B}_n and its cohomology

Abstract

In this paper we prove that the complement to the affine complex arrangement of type \widetilde{B}_n is a K(π, 1) space. We also compute the cohomology of the affine Artin group G of type \widetilde{B}_n with coefficients over several interesting local systems. In particular, we consider the module Q[q^{\pm 1}, t^{\pm 1}], where the first n-standard generators of G act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such representation generalizes the analog 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 with trivial coefficients is derived from the previous one.

arXiv comment21 pages

Cited by in corpus (10)

• Proof of the $K(\pi ,1)$ conjecture for affine Artin groups
• Weighted sheaves and homology of Artin groups
• Some topological problems on the configuration spaces of Artin and Coxeter groups
• On the classifying space of Artin monoids
• Second mod $2$ homology of Artin groups
• Dual structures on Coxeter and Artin groups of rank three
• On the local homology of Artin groups of finite and affine type
• The $K(\pi ,1)$ conjecture for Artin groups of spherical type
• On aspherical configuration Lie groupoids
• The affine Artin group of type ${\tilde{B}}_n$ is virtually poly-free