Gromov’s macroscopic dimension conjecture

Bolotov, Dmitry

doi:10.2140/agt.2006.6.1669

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Gromov's macroscopic dimension conjecture

Dmitry V Bolotov

Algebraic & Geometric Topology 6 (2006) 1669–1676

DOI: 10.2140/agt.2006.6.1669

arXiv: 0904.4886

Abstract

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.

Keywords

closed manifold, universal covering, macroscopic dimension

Mathematical Subject Classification 2000

Primary: 57R19

Secondary: 57R20

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Publication

Received: 2 March 2006

Accepted: 1 September 2006

Published: 14 October 2006

Authors

Dmitry V Bolotov
B Verkin Institute for Low Temperature Physics Lenina ave 47 Kharkov 61103 Ukraine

Volume 6, issue 4 (2006)