Algebraic & Geometric Topology

Gromov's macroscopic dimension conjecture

Dmitry Bolotov

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In this note we construct a closed 4–manifold having torsion-free fundamental group and whose universal covering is of macroscopic dimension 3. This yields a counterexample to Gromov’s conjecture about the falling of macroscopic dimension.

Article information

Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1669-1676.

Received: 2 March 2006
Accepted: 1 September 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R19: Algebraic topology on manifolds
Secondary: 57R20: Characteristic classes and numbers

closed manifold universal covering macroscopic dimension


Bolotov, Dmitry. Gromov's macroscopic dimension conjecture. Algebr. Geom. Topol. 6 (2006), no. 4, 1669--1676. doi:10.2140/agt.2006.6.1669.

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