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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 3, Pages 34–40 (Mi faa3046)  

This article is cited in 2 scientific papers (total in 2 papers)

On macroscopic dimension of rationally inessential manifolds

A. N. Dranishnikov

Department of Mathematics, University of Florida

Abstract: 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 $n$: $\dim_{MC}\widetilde{M}<n$. As a corollary, we obtain the following partial result towards Gromov's conjecture:
\textit{The inequality $\dim_{MC}\widetilde{M}<n$ 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.

DOI: https://doi.org/10.4213/faa3046

Full text: PDF file (181 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:3, 187–191

Bibliographic databases:

UDC: 514.7
Received: 20.01.2011

Citation: A. N. Dranishnikov, “On macroscopic dimension of rationally inessential manifolds”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 34–40; Funct. Anal. Appl., 45:3 (2011), 187–191

Citation in format AMSBIB
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\by A.~N.~Dranishnikov
\paper On macroscopic dimension of rationally inessential manifolds
\jour Funktsional. Anal. i Prilozhen.
\yr 2011
\vol 45
\issue 3
\pages 34--40
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\crossref{https://doi.org/10.4213/faa3046}
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\zmath{https://zbmath.org/?q=an:1271.53043}
\elib{https://elibrary.ru/item.asp?id=20730625}
\transl
\jour Funct. Anal. Appl.
\yr 2011
\vol 45
\issue 3
\pages 187--191
\crossref{https://doi.org/10.1007/s10688-011-0022-9}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053551934}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Dranishnikov, “On Gromov's positive scalar curvature conjecture for duality groups”, J. Topol. Anal., 6:3 (2014), 397–419  crossref  mathscinet  zmath  isi  scopus
    2. Frauenfelder U., Pajitnov A., “Finiteness of
      $$\pi _1$$
      1 -sensitive Hofer–Zehnder capacity and equivariant loop space homology”, J. Fixed Point Theory Appl., 19:1 (2017), 3–15  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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