Volume 6, issue 4 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Gromov's macroscopic dimension conjecture

Dmitry V Bolotov

Algebraic & Geometric Topology 6 (2006) 1669–1676

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