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The K(pi, 1) problem for the affine Artin group of type (B)over-tilde(n) and its cohomology

Callegaro F., Moroni D., Salvetti M.

Affine Artin groups  Group representations  Twisted cohomology  Computational Algebraic Topology 

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.

Source: Journal of the European Mathematical Society (Print) 12 (2010): 1–22. doi:10.471/JEMS/187

Publisher: EMS Publishing House, Zürich


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BibTeX entry
	title = {The K(pi, 1) problem for the affine Artin group of type (B)over-tilde(n) and its cohomology},
	author = {Callegaro F. and Moroni D. and Salvetti M.},
	publisher = {EMS Publishing House, Zürich },
	doi = {10.471/jems/187},
	journal = {Journal of the European Mathematical Society (Print)},
	volume = {12},
	pages = {1–22},
	year = {2010}