Geodesic
Macroscopic dimension and essential manifolds
Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 41-53

Voir la notice de l'article provenant de la source Math-Net.Ru

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{TRSPY_2011_273_a3,
     author = {A. N. Dranishnikov},
     title = {Macroscopic dimension and essential manifolds},
     journal = {Informatics and Automation},
     pages = {41--53},
     publisher = {mathdoc},
     volume = {273},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a3/}
}
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A. N. Dranishnikov. Macroscopic dimension and essential manifolds. Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 41-53. http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a3/