arXiv subjects

Dmitry V. Bolotov

Publications and source records attributed to Dmitry V. Bolotov.

4 recordsLinked to original sources

arXiv2025

Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds

In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation $\mathcal{F}$ of dimension one defined on a closed three-dimensional orientable manifold $M^3$ of negative curvature, which depends on the constants bounded the injectivity radius $inj(M^3)$, the volume $Vol(M^3)$, sectional curvature of the manifold $M^3$ and the mean curvature modulus of the leaves of the foliation $\mathcal{F}$.

math.GT↗

arXiv2025

The $L^2$-norm of the Euler class for Foliations on closed irreducible Riemannian 3-Manifolds

An upper bound for the $L^2$- norm of the Euler class $e(\cal F)$ of an arbitrary transversally orientable foliation $\cal F$ of codimension one, defined on a three-dimensional closed irreducible orientable Riemannian 3-manifold $M^3$ is given in terms of constants bounding the volume, the radius of injectivity, the sectional curvature of $M^3$ and the modulus of mean curvature of the leaves. As a consequence we get that only finitely many cohomolo\-gical classes of the group $H^2(M^3)$ that can be realized by the Euler class $e(\cal F)$ of a two-dimensional transversely oriented foliation $\cal F $ whose leaves have the modulus of mean curvature which is bounded above by the fixed constant $H_0$.

math.GT↗

arXiv2024

On 2-convex non-orientable surfaces in four-dimensional Euclidean space

We prove that a 2-convex closed surface $S\subset E^4$ in the four-dimensional Euclidean space $E^4$, which is either $C^2$-smooth or polyhedral, provided that each vertex is incident to at most five edges, admits a mapping of degree one to a two-dimensional torus, where the degree is assumed to be $\mod 2$ if $S$ is nonorientable. As a corollary, we show that the projective plane and the Klein bottle do not admit such a 2-convex embedding in $E^4$.

math.GT↗

arXiv2017

Foliated Milnor conjecture

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 contains abelian subgroup of finite index. In particular, we confirm the Milnor conjecture for manifolds which are leaves of codimension one nonnegative Ricci curvature foliation of closed manifold.

math.GT↗