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Bulletin of the London Mathematical Society Advance Access originally published online on September 9, 2009
Bulletin of the London Mathematical Society 2009 41(5):859-871; doi:10.1112/blms/bdp063
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© 2009 London Mathematical Society

Gorenstein dimension and proper actions

Abdolnaser Bahlekeh

Department of Mathematics
University of Isfahan
Isfahan
Iran
n_bahlekeh@yahoo.com

Fotini Dembegioti

Department of Mathematics
University of Athens
Panepistimiopolis
GR-157 84 Athens
Greece
fdebeg@math.uoa.gr

Olympia Talelli

Department of Mathematics
University of Athens
Panepistimiopolis
GR-157 84 Athens
Greece

Received 17 May 2008. Revision received 5 May 2009.

We conjecture that a group G admits a finite-dimensional classifying space for proper actions if and only if the Gorenstein projective dimension of G is finite. We verify the one-dimensional case of this conjecture. Some evidence are given for the hypothesis that the Gorenstein projective ZG-modules are precisely Benson's class of cofibrant modules.

2000 Mathematics Subject Classification 20J05, 57N99.

The third author was partially supported by ELKE (grant #70/4/6411).


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