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Callegaro F., Moroni D., Salvetti M. The K(pi, 1) problem for the affine Artin group of type (B)over-tilde(n) and its cohomology. In: Journal of the European Mathematical Society, vol. 12 (1) pp. 1 - 22. EUROPEAN MATHEMATICAL SOC, 2010.
 
 
Abstract
(English)
We prove that the complement to the affine complex arrangement of type (B) over tilde (n) is a K(pi, 1) space. We also compute the cohomology of the affine Artin group G (B) over tilde (n) ( of type (B) over tilde (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) over tilde (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) over tilde (n) with trivial coefficients is derived from the previous one.
URL: http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=12&iss=1&rank=1
DOI: 10.4171/JEMS/187
Subject Affine Artin groups
Group representations
Twisted cohomology
Computational Algebraic Topology
F.2.1 Numerical Algorithms and Problems
F.2.2 Nonnumerical Algorithms and Problems
20J06
20F36
55P20


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