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Transactions of the Moscow Mathematical Society

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On macroscopic dimension of universal coverings of closed manifolds


Author: A. Dranishnikov
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 74 (2013), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2013, 229-244
MSC (2010): Primary 55M30; Secondary 53C23, 57N65
DOI: https://doi.org/10.1090/S0077-1554-2014-00221-1
Published electronically: April 9, 2014
MathSciNet review: 3235798
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a homological characterization of $ n$-manifolds whose universal covering $ \widetilde {M}$ has Gromov's macroscopic dimension $ \dim _{mc}\widetilde {M<n}$. As a result, we distinguish $ \dim _{mc}$ from the macroscopic dimension $ \dim _{MC}$ defined by the author in an earlier paper. We prove the inequality $ \dim _{mc}\widetilde {M} <\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$.


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Additional Information

A. Dranishnikov
Affiliation: Department of Mathematics, University of Florida — and — Steklov Mathematical Institute, Moscow, Russia
Email: dranish@math.ufl.edu

DOI: https://doi.org/10.1090/S0077-1554-2014-00221-1
Keywords: Macroscopic dimension, duality group, amenable group
Published electronically: April 9, 2014
Article copyright: © Copyright 2014 A. Dranishnikov

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