For each subcomplex of the standard CW-structure on any torus, we compute the homology of a certain infinite cyclic regular covering space. In all cases when the homology is finitely generated, we also compute the cohomology ring. For aspherical subcomplexes of the torus, our computation gives the homology of the groups introduced by M. Bestvina and N. Brady in . We compute the cohomological dimension of each of these groups.
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Ian J. Leary, Müge Saadetoğlu, The cohomology of Bestvina–Brady groups. Groups Geom. Dyn. 5 (2011), no. 1, pp. 121–138DOI 10.4171/GGD/118