L-spaces, taut foliations, and graph manifolds

Abstract

If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if ${\pi }_1(Y)$ is not left-orderable.

10 pages, 1 figure; version 3 is accepted version, to appear in Compositio Mathematica

References in corpus (4)

• Floer Simple Manifolds and L-Space Intervals
• Approximating $C^0$-foliations by contact structures
• $C^0$ Approximations of foliations
• L-space intervals for Graph Manifolds and Cables

Cited by in corpus (10)

• Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
• A calculus for bordered Floer homology
• Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
• L-space surgeries on satellites by algebraic links
• Thin links and Conway spheres
• L-spaces, taut foliations and the Whitehead link
• L-space surgeries on 2-component L-space links
• Taut foliations from knot diagrams
• Circular orderability of 3-manifold groups
• L-spaces, taut foliations and fibered hyperbolic two-bridge links