Foliations of codimension one and Milnor's 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
E-mail: bolotov@ilt.kharkov.ua

Received May 30, 2017, revised June 31, 2017

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.

Mathematics Subject Classification 2010: 53A05. Key words: codimension one foliation, fundamental group, holonomy, Ricci curvature.