JournalsggdVol. 6 , No. 3pp. 485–531

Cohomology computations for Artin groups, Bestvina–Brady groups, and graph products

  • Michael W. Davis

    Ohio State University, Columbus, USA
  • Boris Okun

    University of Wisconsin at Milwaukee, USA
Cohomology computations for Artin groups, Bestvina–Brady groups, and graph products cover
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Abstract

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,
  • the L2L^2-Betti numbers of Bestvina–Brady groups of type FP over Q\mathbb{Q}, and of graph products of groups,
  • the weighted L2L^2-Betti numbers of graph products of Coxeter groups.

In the case of arbitrary graph products there is an additional proviso: either all factors are infinite or all are finite.

Cite this article

Michael W. Davis, Boris Okun, Cohomology computations for Artin groups, Bestvina–Brady groups, and graph products. Groups Geom. Dyn. 6 (2012), no. 3 pp. 485–531

DOI 10.4171/GGD/164