On Lipschitz cohomology of aspherical manifolds

We introduce the notion of Lipschitz cohomology classes of a group with local coefficients and reduce the Novikov higher signature conjecture for a group $\mathrm{\Gamma }$ to the question whether the Berstein-Schwarz class ${\beta }_{\mathrm{\Gamma }}\in H^1(\mathrm{\Gamma },I(\mathrm{\Gamma }))$ is Lipschitz.