D.Bolotov (Joint work with A. Dranishnikov)

The Gromov's macroscopic dimension conjecture for PSC - manifolds
and a fundamental group

We prove the Gromov conjecture on the macroscopic dimension of the
universal covering of a closed spin manifold with a positive scalar
curvature under the following assumptions on the fundamental group: 1.
The Strong Novikov Conjecture holds for $\pi$. 2. The natural map
$per:ko_n(B\pi)\to KO_n(B\pi)$ is injective.