On macroscopic dimension of universal coverings of closed manifolds
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 279-296
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We give a homological characterization of $n$-manifolds whose universal covering $\widetilde{M}$ has Gromov’s macroscopic dimension $\mathrm{dim}_{mc}\widetilde{M}$. As the result we distinguish $\mathrm{dim}_{mc}$ from the macroscopic dimension $\mathrm{dim}_{MC}$ defined by the author [7]. We prove the inequality $\mathrm{dim}_{mc}\widetilde{M}\mathrm{dim}_{MC}\widetilde{M}=n$ for every closed $n$-manifold $M$ whose fundamental group $\pi$ is a geometrically finite amenable duality group with the cohomological dimension $cd(\pi)>n$.
References: 14 entries.
@article{MMO_2013_74_2_a4,
author = {A. Dranishnikov},
title = {On macroscopic dimension of universal coverings of closed manifolds},
journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
pages = {279--296},
publisher = {mathdoc},
volume = {74},
number = {2},
year = {2013},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MMO_2013_74_2_a4/}
}
A. Dranishnikov. On macroscopic dimension of universal coverings of closed manifolds. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 279-296. http://geodesic.mathdoc.fr/item/MMO_2013_74_2_a4/