Analytic Pontryagin duality

Johnny Lim
2019 Journal of Geometry and Physics  
Let X be a smooth compact manifold. We propose a geometric model for the group K^0(X,R/Z). We study a well-defined and non-degenerate analytic duality pairing between K^0(X,R/Z) and its Pontryagin dual group, the Baum-Douglas geometric K-homology K_0(X), whose pairing formula comprises of an analytic term involving the Dai-Zhang eta-invariant associated to a twisted Dirac-type operator and a topological term involving a differential form and some characteristic forms. This yields a robust
more » ... lued invariant. We also study two special cases of the analytic pairing of this form in the cohomology group H^1(X,R/Z) and H^2(X,R/Z).
doi:10.1016/j.geomphys.2019.103483 fatcat:qoywd6lqdba57cvic5zhbwnyeq