Wednesday 22 February 2017, 16:00 - 17:00 in HG03.085
Irakli Patchkoria (Universität Bonn)
Proper G-spectra, geometric group theory and TC
We will start by discussing some classical dimension invariants from geometric group theory and their relations with homotopy theory. This will lead to the notion of a proper G-spectrum for any infinite discrete group G. We will discuss basic properties or proper G-spectra and indicate how one develops proper equivariant stable homotopy theory with them. This is a part of a joint project with Degrijse, Hausmann, Lück and Schwede. As the first application we will provide a geometric characterization of the virtual cohomological dimension of a virtually torsion free group. We will see what this gives on an explicit example of a certain Coxeter group. This is a part of a joint work with Barcenas and Degrijse. As the second application of the theory of proper G-spectra, we will present the connection between proper Q_p/Z_p-spectra and topological cyclic homology. In particular, we will see how proper Q_p/Z_p-spectra avoid p-completions.