Analytic Pontryagin duality

Johnny Lim  (University of Adelaide)

15:30-16:45, Oct 26, 2019   Science Building A510

Abstract:

Let X be a smooth compact manifold. The Universal Coefficient Theorem in K-theory with coefficients in R/Z asserts that there is an isomorphism between the R/Z K-theory group Ki(R/Z) and the Hom group Hom(Ki(X),R/Z). We study an explicit analytic duality pairing in the even case which implements the isomorphism. We propose a model of the group K0(X, R/Z). Together with the even Baum-Douglas geometric K-homology K0(X), we formulate an analytic pairing comprises of the Dai-Zhang eta-invariant of a certain Dirac-type operator and a topological term. This analytic pairing is well-defined and non-degenerate, thus giving a robust R/Z invariant. As a motivation, we study two special cases of the analytic pairing in cohomology.