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- W2952549722 abstract "The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type B_n with coefficients over the module Q[q^{pm 1},t^{pm 1}]. Here the first (n-1) standard generators of the group act by (-q)-multiplication, while the last one acts by (-t)-multiplication. The proof uses some technical results from previous papers plus computations over a suitable spectral sequence. The remaining cases follow from an application of Shapiro's lemma, by considering some well-known inclusions: we obtain the rational cohomology of the Artin group of affine type tilde{A}_{n} as well as the cohomology of the classical braid group {Br}_{n} with coefficients in the n-dimensional representation presented in cite{tong}. The topological counterpart is the explicit construction of finite CW-complexes endowed with a free action of the Artin groups, which are known to be K(pi,1) spaces in some cases (including finite type groups). Particularly simple formulas for the Euler-characteristic of these orbit spaces are derived." @default.
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- W2952549722 date "2007-05-19" @default.
- W2952549722 modified "2023-10-01" @default.
- W2952549722 title "Cohomology of affine Artin groups and applications" @default.
- W2952549722 hasPublicationYear "2007" @default.
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