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.
The $K(pi,1)$ problem for the Artin group of type $tilde{B}_n$ and its cohomology
SALVETTI, MARIO;CALLEGARO, FILIPPO GIANLUCA;
2010-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
