Stable finiteness properties of infinite discrete groups. Issue 4 (8th December 2017)
- Record Type:
- Journal Article
- Title:
- Stable finiteness properties of infinite discrete groups. Issue 4 (8th December 2017)
- Main Title:
- Stable finiteness properties of infinite discrete groups
- Authors:
- Bárcenas, Noé
Degrijse, Dieter
Patchkoria, Irakli - Abstract:
- Abstract: Let G be an infinite discrete group. A classifying space for proper actions of G is a proper G ‐CW complex X such that the fixed point sets X H are contractible for all finite subgroups H of G . In this paper we consider the stable analogue of the classifying space for proper actions in the category of proper G ‐spectra and study its finiteness properties. We investigate when G admits a stable classifying space for proper actions that is finite or of finite type and relate these conditions to the compactness of the sphere spectrum in the homotopy category of proper G ‐spectra and to classical finiteness properties of the Weyl groups of finite subgroups of G . Finally, if the group G is virtually torsion‐free we also show that the smallest possible dimension of a stable classifying space for proper actions coincides with the virtual cohomological dimension of G, thus providing the first geometric interpretation of the virtual cohomological dimension of a group.
- Is Part Of:
- Journal of topology. Volume 10:Issue 4(2017)
- Journal:
- Journal of topology
- Issue:
- Volume 10:Issue 4(2017)
- Issue Display:
- Volume 10, Issue 4 (2017)
- Year:
- 2017
- Volume:
- 10
- Issue:
- 4
- Issue Sort Value:
- 2017-0010-0004-0000
- Page Start:
- 1169
- Page End:
- 1196
- Publication Date:
- 2017-12-08
- Subjects:
- 20J05 -- 55P42 -- 55P91 (primary)
Topology -- Periodicals
514.05 - Journal URLs:
- http://jtopol.oxfordjournals.org/current.dtl ↗
http://ukcatalogue.oup.com/ ↗ - DOI:
- 10.1112/topo.12035 ↗
- Languages:
- English
- ISSNs:
- 1753-8416
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5069.590000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 13292.xml