Flat bundles, von Neumann algebras and $K$-theory with $\mathbb{R}/\mathbb{Z}$-coefficients

Paolo Antonini, Sara Azzali, Georges Skandalis

Let $M$ be a closed manifold and $\alpha :{\pi }_1(M)\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\alpha ]$ in the $K$-theory of $M$ with $\R/\…