Taut foliations of 3-manifolds with Heegaard genus two
Tao Li

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 be a closed, orientable, and irreducible 3-manifold with Heegaard genus two. We prove that if the fundamental group of is left-orderable then admits a co-orientable taut foliation.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology
