Stability for the Cohomology of Artin Groups
نویسندگان
چکیده
منابع مشابه
The `-cohomology of Artin Groups
For each Artin group we compute the reduced `cohomology of (the universal cover of) its “Salvetti complex”. This is a CW-complex which is conjectured to be a model for the classifying space of the Artin group. In the many cases when this conjecture is known to hold our calculation describes the reduced `-cohomology of the Artin group.
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The result of this paper is the determination of the cohomology of Artin groups of type An, Bn and Ãn with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type Bn with coefficients over the module Q[q±1, t±1]. Here the first n− 1 standard generators of the group act by (−q)-multiplication, while the last one acts by (−t)-multipl...
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We consider two natural embeddings between Artin groups: the group GÃn−1 of type Ãn−1 embeds into the group GBn of type Bn ; GBn in turn embeds into the classical braid group Brn+1 := GAn of type An . The cohomologies of these groups are related, by standard results, in a precise way. By using techniques developed in previous papers, we give precise formulas (sketching the proofs) for the cohom...
متن کاملCohomology computations for Artin groups, Bestvina–Brady groups, and graph products
We compute: the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), of Bestvina–Brady groups of type FP, and of graph products of groups, theL-Betti numbers of Bestvina–Brady groups of type FP overQ, and of graph products of groups, the weighted L-Betti numbers of graph products of Coxeter groups. In the case of arbitrary graph products...
متن کاملThe Cohomology of Right Angled Artin Groups with Group Ring Coefficients
We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1999
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1820