Algebra/Topology seminar

Speaker: Irakli Patchkoria

Title: Proper equivariant stable homotopy theory

Abstract: We construct a symmetric monoidal stable model category of proper G-spectra where G is any Lie group. The homotopy category of this model category is generated as a triangulated category by the G-orbits with compact isotropy and admits restriction functors to genuine H-spectra for any compact subgroup H of G. When G is discrete, a proper G-spectrum gives rise to a G-Mackey functor by taking homotopy groups. If G has enough bundle representations, then on finite proper G-CW complexes we identify the cohomology theory represented by the sphere G-spectrum as Lück's equivariant stable cohomotopy. Further we will provide an algebraic model for rational proper G-spectra for a discrete group G. If time permits we will also discuss relations to equivariant K-theory. All this is joint work with Degrijse, Hausmann, Lück and Schwede.