Foliations of codimension one and the Milnor conjecture

Dmitry V. Bolotov

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

Abstract: We prove that a fundamental group of leaves of a codimension one $C^2$-foliation with nonnegative Ricci curvature on a closed Riemannian manifold is finitely generated and almost Abelian, i.e., it contains finitely generated Abelian subgroup of finite index. In particular, we confirm the Milnor conjecture for manifolds which are leaves of a codimension one foliation with nonnegative Ricci curvature on a closed Riemannian manifold.

Key words and phrases: codimension one foliation, fundamental group, holonomy, Ricci curvature.

MSC: 53A05

Received: 30.05.2017
Revised: 31.07.2017

Language: English

DOI: 10.15407/mag14.02.119