Bonn Topology Group - Abstracts

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June 4th 2019
Kralle Patchkoria (University of Aberdeen, Scotland): Proper equivariant stable homotopy theory


In this talk we will discuss a setup for equivariant stable homotopy theory for proper actions of not necessarily compact Lie groups. Given a Lie group G, we consider the category of orthogonal spectra with G-action together with the class of morphisms inducing genuine equivalences after restricting to compact subgroups. Associated homotopy theory of proper G-spectra has many interesting features. It is compactly generated by suspension spectra of the orbits G/H, where H is compact. Equivariant stable cohomotopy of Lück, equivariant K-theory of Lück and Oliver and Bredon cohomology are naturally represented in the homotopy category of proper G-spectra for G discrete. The cohomology theories represented by proper G-spectra are naturally graded by equivariant vector bundles over the classifying space for proper G-actions. This generalizes the RO(G)-grading structure from the compact to the non-compact case. At the end we will mention several computations and applications.
This is all joint with D. Degrijse, M. Hausmann, W. Lück and S. Schwede.

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