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Tr. Mosk. Mat. Obs., 2013, Volume 74, Issue 2, Pages 279–296 (Mi mmo549)  

This article is cited in 4 scientific papers (total in 4 papers)

On macroscopic dimension of universal coverings of closed manifolds

A. Dranishnikovab

a Department of Mathematics, University of Florida, USA
b Steklov Mathematical Institute, Moscow, Russia

Abstract: We give a homological characterization of $n$-manifolds whose universal covering $\widetilde{M}$ has Gromovs macroscopic dimension $\mathrm{dim}_{mc}\widetilde{M}<n$. 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.

Key words and phrases: macroscopic dimension, duality group, amenable group.

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English version:
Transactions of the Moscow Mathematical Society, 2013, 74, 229–244

Bibliographic databases:

UDC: 514.7
MSC: Primary 55M30; Secondary 53C23, 57N65
Received: 13.05.2013
Language:

Citation: A. Dranishnikov, “On macroscopic dimension of universal coverings of closed manifolds”, Tr. Mosk. Mat. Obs., 74, no. 2, MCCME, M., 2013, 279–296; Trans. Moscow Math. Soc., 74 (2013), 229–244

Citation in format AMSBIB
\Bibitem{Dra13}
\by A.~Dranishnikov
\paper On macroscopic dimension of universal coverings of closed manifolds
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 2
\pages 279--296
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo549}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3235798}
\zmath{https://zbmath.org/?q=an:1310.55005}
\elib{https://elibrary.ru/item.asp?id=21369372}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 229--244
\crossref{https://doi.org/10.1090/S0077-1554-2014-00221-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960095158}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dranishnikov A., “on Gromov'S Positive Scalar Curvature Conjecture For Duality Groups”, J. Topol. Anal., 6:3 (2014), 397–419  crossref  mathscinet  zmath  isi  elib  scopus
    2. Blank M., Diana F., “Uniformly Finite Homology and Amenable Groups”, Algebr. Geom. Topol., 15:1 (2015), 467–492  crossref  mathscinet  zmath  isi  scopus
    3. M. Marcinkowski, “Gromov positive scalar curvature conjecture and rationally inessential macroscopically large manifolds”, J. Topol., 9:1 (2016), 105–116  crossref  mathscinet  zmath  isi  scopus
    4. D. Bolotov, A. Dranishnikov, “On Gromov's conjecture for totally non-spin manifolds”, J. Topol. Anal., 8:4 (2016), 571–587  crossref  mathscinet  zmath  isi  scopus
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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