On Gromov's marcroscopic dimension conjecture

We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin $n$-manifold with a positive scalar curvature under the assumption that the fundamental group of a manifold $\pi$ satisfies the Strong Novikov conjecture and the homomorphis from the connective real K-theory of $B\pi$ to the periodic K-theory is injective in dimension $n$.