## On macroscopic dimension of rationally inessential manifolds.(English. Russian original)Zbl 1271.53043

Funct. Anal. Appl. 45, No. 3, 187-191 (2011); translation from Funkts. Anal. Prilozh. 45, No. 3, 34-40 (2011).
Summary: We show that, for a rationally inessential orientable closed $$n$$-manifold $$M$$ whose fundamental group is a duality group, the macroscopic dimension of its universal cover $$\widetilde M$$ is strictly less than $$n:\dim_{MC}\widetilde M<n$$. As a corollary, we obtain the following partial result towards Gromov’s conjecture:
The inequality $$\dim_{MC}\widetilde M<n$$ holds for the universal cover $$\widetilde M$$ of a closed spin $$n$$-manifold $$M$$ with a positive scalar curvature metric if the fundamental group $$\pi_1(M)$$ is a duality group satisfying the analytic Novikov conjecture.

### MSC:

 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

### Keywords:

macroscopic dimension; inessential manifold; duality group
Full Text:

### References:

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