Differential characters in \(K\)-theory (Q2507691)

The authors define a new notion of \(\mathbb{R}/\mathbb{Z}\)-differential \(K\)-characters \(\hat{K}^*(X)\) and show that the eta invariant of Atyiah-Patodi-Singer is an \(\mathbb{R}/\mathbb{Z}\)-secondary invariant in this theory. Their main ingredient is to use the Baum-Douglas picture of \(K\)-homology [\textit{P. Baum} and \textit{R. G. Douglas}, Proc. Symp. Pure Math. 38, Part 1, Kingston/Ont. 1980, 117--173 (1982; Zbl 0532.55004)], and under their construction, the group \(K(X,\mathbb{R}/\mathbb{Z})\) of \(\mathbb{R}/\mathbb{Z}\)-K-theory is a sub-group of \(\hat{K}^*(X)\).