Taut foliations of 3-manifolds with Heegaard genus two

TL;DR

This paper proves that closed, orientable, irreducible 3-manifolds with Heegaard genus two and left-orderable fundamental groups admit co-orientable taut foliations, linking algebraic properties to geometric structures.

Contribution

It establishes a new connection between the left-orderability of the fundamental group and the existence of taut foliations in genus two 3-manifolds.

Findings

Left-orderable fundamental groups imply taut foliations in genus two manifolds

The result applies to closed, orientable, irreducible 3-manifolds

Provides a criterion linking algebraic and geometric properties

Abstract

Let $M$ be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of $M$ is left-orderable then $M$ admits a co-orientable taut foliation.