Geodesic
On macroscopic dimension of rationally inessential manifolds
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 3, pp. 34-40

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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.}
Keywords: macroscopic dimension, inessential manifold, duality group. 
@article{FAA_2011_45_3_a3,
     author = {A. N. Dranishnikov},
     title = {On macroscopic dimension of rationally inessential manifolds},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {34--40},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_3_a3/}
}
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A. N. Dranishnikov. On macroscopic dimension of rationally inessential manifolds. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 3, pp. 34-40. http://geodesic.mathdoc.fr/item/FAA_2011_45_3_a3/