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December 02, 2021
Thursday, December 02
GAP Seminar
Time: 10:30
Speaker: Luuk Verhoeven (Western)
Title: "Factorization of Dirac operators along a submersion"
Room: MC 108

Abstract: Spectral triples (A,H,D) can be interpreted as unbounded representatives for classes in KK-theory, specifically in KK(A,C). It therefore seems natural to investigate if, and how, constructions from KK-theory are reflected back in noncommutative geometry. In this talk we will look at a specific case of this; given a submersion pi:M->B there is a class, pi!, in KK(C(M), C(B)) such that there is a Kasparov product [M] = pi! x [B]. In this talk we will cover an article by W. van Suijlekom and J. Kaad on how this Kasparov product works at the level of spectral triples and correspondences. It turns out that the factorization is exact, up to a curvature term.