Dimension invariants for groups admitting a cocompact model for proper actions
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Let G be a group that admits a cocompact classifying space for proper actions X. We derive a formula for the Bredon cohomological dimension for proper actions of G in terms of the relative cohomology with compact support of certain pairs of subcomplexes of X.
We use this formula to compute the Bredon cohomological dimension for
proper actions of fundamental groups of non-positively curved simple
complexes of finite groups. As an application we show that if a
virtually torsion-free group acts properly and chamber transitively on a
building, its virtual cohomological dimension coincides with its Bredon
cohomological dimension. This covers the case of Coxeter groups and
graph products of finite groups.
Original language | English |
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Journal | Journal fuer die Reine und Angewandte Mathematik |
Volume | 721 |
Pages (from-to) | 233–249 |
ISSN | 0075-4102 |
DOIs | |
Publication status | Published - 2016 |
ID: 162904566