Geodesic
Macroscopic dimension and essential manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 41-53

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M. Gromov asked whether the macroscopic dimension of rationally essential $n$-dimensional manifolds equals $n$. We show that the answer depends only on the corresponding group homology class and give an affirmative answer for certain classes. In particular, the answer is positive for manifolds with amenable fundamental groups. 
@article{TM_2011_273_a3,
     author = {A. N. Dranishnikov},
     title = {Macroscopic dimension and essential manifolds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_273_a3/}
}
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A. N. Dranishnikov. Macroscopic dimension and essential manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 41-53. http://geodesic.mathdoc.fr/item/TM_2011_273_a3/