\(K\)-theory with \(\mathbb{R}/\mathbb{Z}\) coefficients and von Neumann algebras (Q864978)

A von Neumann realization of K-theory for spaces \(X\) with \(\mathbb R/\mathbb Z\) coefficients and its equivalence with the Atiyah-Patodi-Singer and Karoubi realizations of the K-theory \(K^1(X, \mathbb R/\mathbb Z)\) is discussed. Furthermore, an index pairing associated with \(K^1(X, \mathbb R/\mathbb Z)\) is constructed. Minor errors are found in this article, especially, in the references. Also, the item \([T]\) is not found there.