On fibering compact manifold over the circle

TL;DR

This paper proves that any compact manifold with an SL(n;R)-foliation necessarily admits a fibration over the circle S^1, revealing a topological structure linked to the foliation.

Contribution

It establishes a new topological classification result connecting SL(n;R)-foliations to circle fibrations on compact manifolds.

Findings

Any compact manifold with an SL(n;R)-foliation is fibered over S^1

The foliation imposes a circle bundle structure on the manifold

The result links foliation properties to global topological features

Abstract

In this paper, we show that any compact manifold that carries a SL(n;R)-foliation is fibered on the circle S^1.