researchseminars.org

Ulrich Bunke (Universität Regensburg)
2023-05-24 19:00 - 20:00 UTC | https://researchseminars.org/talk/NYC-NCG/132/
Title: A homotopical view on $K$ and $KK$-theory for $C^{*}$-algebras (https://researchseminars.org/talk/NYC-NCG/132/)
by Ulrich Bunke (Universität Regensburg) as part of Noncommutative geometry in NYC

Abstract
The goal of this talk is to motivate the consideration of spectrum-valued K-theory for $C^{*}$-algebras. To this end I will discuss some examples where the spectrum-valued functor helps to simplify classical statements and their justification. I will then explain how to construct a spectrum-valued $K$-theory functor using a homotopical refinement of KK-theory. Accepting the language of $\infty$-categories, the latter can be obtained in a straightforward way by forcing the desired universal properties.
