Nordic Topology Meeting 
Friday, August 28, 09:00 - 09:45

Irakli Patchkoria: Geometric meaning of the virtual cohomological dimension of a group.

I will introduce a stable model category of proper G-spectra where G is an infinite discrete group and discuss the properties of its triangulated homotopy category. This is joint work with Degrijse, Hausmann, Luck and Schwede. As an application of this setup I will also discuss a second project, joint with Barcenas and Degrijse, where we define a notion of stable geometric dimension for proper actions of G. We prove that this notion of dimension coincides with the Mackey cohomological dimension of G. If G is virtually torsion free, the Mackey cohomological dimension is known to equal the virtual cohomological dimension of G. Hence we obtain a geometric interpretation of the virtual cohomological dimension of G.