An Introduction to K-homology and KK-theory (Lecture 1)

Ryszard Nest  (University of Copenhagen)

15:30-17:00, April 13, 2022   Zoom Meeting ID: 614 9918 4088 (Passcode: 646373)

Abstract:

Part I. An introduction to K-homology: 1. Definitions, K-homology and extensions, 2. Technical theorems (Stinespring, Voiculescu Weyl-von Neumann, Kasparov technical theorem), the technology of essential representations, 3. Paschke duality, excision and Bott periodicity, 4. BDF theory. Part II. An introduction to KK-theory: 1. Basic definitions and properties of KK-functors, 2. Kasparov product (Cuntz and Connes-Skandalis pictures), 3. Group actions and assembly map, γ-element, 4. Homological algebra in KK, UCT revisited and strong Baum-Connes conjecture.

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