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

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

2007-05-19

arxiv.org/abs/0705.2830v1

Mathematics

Algebraic Topology

21 pages

Scientific paper

In this paper we prove that the complement to the affine complex arrangement of type \widetilde{B}_n is a K(\pi, 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.

Affiliated with

Also associated with

No associations

Rating

The K(π, 1) problem for the affine Artin group of type \widetilde{B}_n and its cohomology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The K(π, 1) problem for the affine Artin group of type \widetilde{B}_n and its cohomology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The K(π, 1) problem for the affine Artin group of type \widetilde{B}_n and its cohomology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-431332