Foliated Milnor conjecture

TL;DR

This paper proves that the fundamental group of a codimension one nonnegative Ricci curvature foliation on a closed manifold is finitely generated and almost abelian, confirming the Milnor conjecture in this setting.

Contribution

It establishes the Milnor conjecture for manifolds that are leaves of codimension one nonnegative Ricci curvature foliations on closed manifolds.

Findings

Fundamental groups are finitely generated.

Fundamental groups are almost abelian.

Milnor conjecture is confirmed for this class of manifolds.

Abstract

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.