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 [3]. We compute the cohomological dimension of each of these groups.
1
University of Southampton, UK
2
Eastern Mediterranean University, Gazimağusa, North Cyprus, Turkey
Ian J. Leary; Müge Saadetoğlu. The cohomology of Bestvina–Brady groups. Groups, geometry, and dynamics, Tome 5 (2011) no. 1, pp. 121-138. doi: 10.4171/ggd/118
@article{10_4171_ggd_118,
author = {Ian J. Leary and M\"uge Saadeto\u{g}lu},
title = {The cohomology of {Bestvina{\textendash}Brady} groups},
journal = {Groups, geometry, and dynamics},
pages = {121--138},
year = {2011},
volume = {5},
number = {1},
doi = {10.4171/ggd/118},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/118/}
}
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AU - Ian J. Leary
AU - Müge Saadetoğlu
TI - The cohomology of Bestvina–Brady groups
JO - Groups, geometry, and dynamics
PY - 2011
SP - 121
EP - 138
VL - 5
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/118/
DO - 10.4171/ggd/118
ID - 10_4171_ggd_118
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