8 citations · 8 across the 5 of their papers we have counts for
6 papers
On 2-convex non-orientable surfaces in four-dimensional Euclidean space
Dmitry V. Bolotov
We prove that a 2-convex closed surface in the four-dimensional Euclidean space , which is either -smooth or polyhedral, provided that each vertex is incid…
The -norm of the Euler class for Foliations on closed irreducible Riemannian 3-Manifolds
Dmitry V. Bolotov
An upper bound for the - norm of the Euler class of an arbitrary transversally orientable foliation of codimension one, defined on a three-dimensional clo…
Foliated Milnor conjecture
Dmitry V. Bolotov
We prove that a fundamental group of codimension one nonnegative Ricci curvature C2-foliation of a closed Riemannian manifold is finitely generated and almost abelian, i.e. it cont…
On Gromov's conjecture for totally non-spin manifolds
Dmitry Bolotov, Alexander Dranishnikov
Gromov's Conjecture states that for a closed -manifold with positive scalar curvature the macroscopic dimension of its universal covering satisfies the inequality…
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…
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…