KK-theory with real coefficients, traces, and discrete group actions

Abstract: The groups of KK-theory were introduced by Kasparov in the 1980’s and have important applications to many geometric and topological problems which are tackled by C*-algebraic techniques.

In this talk, we investigate KK-theory groups with coefficients in $\mathbb R$. By construction, the adding of real coefficients provides natural receptacles for classes coming from traces on $C^*$-algebras. We focus on applications to the study of discrete groups actions on $C^*$-algebras. We show that in equivariant KK-theory with coefficients one can "localize at the unit element“ of the discrete group, and this procedure has interesting consequences on the Baum–Connes isomorphism conjecture. Based on joint works with Paolo Antonini and Georges Skandalis.

Mathematics

Audience: researchers in the topic

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.