Geometry & Topology

On macroscopic dimension of rationally essential manifolds

Alexander Dranishnikov

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We construct a counterexamples in dimensions n>3 to Gromov’s conjecture that the macroscopic dimension of rationally essential n–dimensional manifolds equals n.

Article information

Geom. Topol., Volume 15, Number 2 (2011), 1107-1124.

Received: 29 April 2010
Revised: 11 April 2011
Accepted: 8 May 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 20J06: Cohomology of groups 55N91: Equivariant homology and cohomology [See also 19L47] 55M10: Dimension theory [See also 54F45] 57N65: Algebraic topology of manifolds

macroscopic dimension essential manifold


Dranishnikov, Alexander. On macroscopic dimension of rationally essential manifolds. Geom. Topol. 15 (2011), no. 2, 1107--1124. doi:10.2140/gt.2011.15.1107.

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