Left orderability and taut foliations with one-sided branching

TL;DR

This paper proves that for certain 3-manifolds with specific taut foliations, their fundamental groups are left orderable, linking foliation properties to algebraic group orderability.

Contribution

It establishes a new connection between taut foliations with one-sided branching and the left orderability of the manifold's fundamental group.

Findings

Fundamental group of the manifold is left orderable.

Connects foliation properties with algebraic orderability.

Advances understanding of 3-manifold topology and group theory.

Abstract

For a closed orientable irreducible $3$-manifold $M$ that admits a co-orientable taut foliation with one-sided branching, we show that $\pi_1(M)$ is left orderable.