Dimension invariants for groups admitting a cocompact model for proper actions
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Dimension invariants for groups admitting a cocompact model for proper actions. / Degrijse, Dieter Dries; Martínez-Pérez, Conchita .
I: Journal fuer die Reine und Angewandte Mathematik, Bind 721, 2016, s. 233–249.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Dimension invariants for groups admitting a cocompact model for proper actions
AU - Degrijse, Dieter Dries
AU - Martínez-Pérez, Conchita
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
U2 - 10.1515/crelle-2014-0061
DO - 10.1515/crelle-2014-0061
M3 - Journal article
VL - 721
SP - 233
EP - 249
JO - Journal fuer die Reine und Angewandte Mathematik
JF - Journal fuer die Reine und Angewandte Mathematik
SN - 0075-4102
ER -
ID: 162904566