Abstract
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_{\widetilde B_n} (of type \widetilde 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_{\widetilde 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_{\widetilde B_n} with trivial coefficients is derived from the previous one.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
