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Differential characters in \(K\)-theory. (English) Zbl 1138.58007

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 [P. Baum and 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 \(\hat{K}^*(X)\).
Reviewer: Xiaonan Ma (Paris)

MSC:

58J28 Eta-invariants, Chern-Simons invariants

Citations:

Zbl 0532.55004
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References:

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