Equivariant KK-theory and model categoriesOberseminar Global Analysis and Operator Algebras

by Anupam Datta (Uni Bonn)

Tuesday Jan 7, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Seminarraum 0.008 (Mathezentrum)

KK-theory can be seen as a homotopy theory for C*-algebras. It is plausible to ask whether it can be cast in the framework of abstract homotopy theory. In the non-equivariant case, Joachim-Johnson showed in 2007 that KK-groups are in fact the homotopy groups of a stable model structure on pro-C*-algebras. I will discuss similar results in the equivariant case, with a locally compact group action on the algebras involved. Some new techniques involving universal equivariant algebras were needed in the construction which would also be discussed. Lastly, a comparison could be made to the more recent infinity categorical equivariant KK-theory à la Bunke.

This is joint work with Michael Joachim.