Compact Lie algebras, transversely Lie foliations and fibrations

TL;DR

This paper investigates Lie foliations on compact manifolds with compact Lie groups, improving classical results on fibrations and exploring implications for manifolds with amenable fundamental groups.

Contribution

It advances the understanding of Lie foliations by refining existing theorems on fibrations and analyzing their behavior in the context of amenable fundamental groups.

Findings

Enhanced conditions for the existence of fibrations in Lie foliations.

Application of results to manifolds with amenable fundamental groups.

Improved classical theorems on Lie foliations and fibrations.

Abstract

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable fundamental group.