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math.GT2009★ 8 cited
Gromov's macroscopic dimension conjecture
Dmitry Bolotov
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 Grom…
math.GT2009
On Gromov's scalar curvature conjecture
Dmitry Bolotov, Alexander Dranishnikov
We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on…