Flat bundles, von Neumann algebras and $K$-theory with $\R/\Z$-coefficients
Flat bundles, von Neumann algebras and $K$-theory with $\R/\Z$-coefficients
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 $\R/\Z$-coefficients. To that end, it is convenient to describe the $\R/\Z$-$K$-theory as a relative $K$-theory with respect to the inclusion …