Dimension invariants for groups admitting a cocompact model for proper actions
-
Dieter Degrijse
and
Conchita Martínez-Pérez
Abstract
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.
Funding source: Danmarks Grundforskningsfond
Award Identifier / Grant number: Centre for Symmetry and Deformation (DNRF92)
Funding source: Ministerio de Educación, Cultura y Deporte
Award Identifier / Grant number: MTM2010-19938-C03-03
Funding statement: The first author was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the second by Gobierno de Aragón, European Regional Development Funds and Ministerio de Educación, Cultura y Deporte through MTM2010-19938-C03-03.
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Singularities with 𝔾m-action and\break the log minimal model program for ℳ¯g
- Normal functions, Picard--Fuchs equations, and elliptic fibrations on K3 surfaces
- Degrees of strongly special subvarieties and the André–Oort conjecture
- Ambitoric geometry I: Einstein metrics and extremal ambikähler structures
- The closure of spectral data for constant mean curvature tori in 𝕊3
- Modular p-adic L-functions attached to real quadratic fields and arithmetic applications
- Dimension invariants for groups admitting a cocompact model for proper actions
Articles in the same Issue
- Frontmatter
- Singularities with 𝔾m-action and\break the log minimal model program for ℳ¯g
- Normal functions, Picard--Fuchs equations, and elliptic fibrations on K3 surfaces
- Degrees of strongly special subvarieties and the André–Oort conjecture
- Ambitoric geometry I: Einstein metrics and extremal ambikähler structures
- The closure of spectral data for constant mean curvature tori in 𝕊3
- Modular p-adic L-functions attached to real quadratic fields and arithmetic applications
- Dimension invariants for groups admitting a cocompact model for proper actions
