On macroscopic dimension of rationally inessential manifolds

A. N. Dranishnikov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 3, pp. 34-40.

Résumé

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 $n$: $\dim_{MC}\widetilde{M}$. As a corollary, we obtain the following partial result towards Gromov's conjecture: \textit{The inequality $\dim_{MC}\widetilde{M}$ 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.}

Détail

Keywords: macroscopic dimension, inessential manifold, duality group.

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