Geodesic
Gromov’s macroscopic dimension conjecture
Bolotov, Dmitry1
1B Verkin Institute for Low Temperature Physics, Lenina ave 47, Kharkov 61103, Ukraine
Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1669-1676
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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.

DOI : 10.2140/agt.2006.6.1669
Keywords: closed manifold, universal covering, macroscopic dimension

Bolotov, Dmitry  1

1 B Verkin Institute for Low Temperature Physics, Lenina ave 47, Kharkov 61103, Ukraine 
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Bolotov, Dmitry. Gromov’s macroscopic dimension conjecture. Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1669-1676. doi: 10.2140/agt.2006.6.1669

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