# L-spaces, taut foliations, and graph manifolds

@article{Hanselman2020LspacesTF,
title={L-spaces, taut foliations, and graph manifolds},
author={Jonathan Hanselman and Jacob Rasmussen and Sarah Dean Rasmussen and Liam Watson},
journal={Compositio Mathematica},
year={2020},
volume={156},
pages={604 - 612}
}
• Published 24 August 2015
• Mathematics
• Compositio Mathematica
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 $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.
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## References

SHOWING 1-10 OF 42 REFERENCES
Slope detection, foliations in graph manifolds, and L-spaces
• Mathematics
• 2015
A graph manifold rational homology $3$-sphere $W$ with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut
Approximating C0-foliations by contact structures
We show that any co-orientable foliation of dimension two on a closed orientable 3-manifold with continuous tangent plane field can be C0-approximated by both positive and negative contact structures
L-space intervals for graph manifolds and cables
We present a graph manifold analog of the Jankins–Neumann classification of Seifert fibered spaces over $S^{2}$ admitting taut foliations, providing a finite recursive formula to compute the L-space
On L-spaces and left-orderable fundamental groups
• Mathematics
• 2011
Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions
$C^0$ Approximations of foliations
• Mathematics
• 2015
Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is
Approximating $C^{1,0}$-foliations
• Mathematics
• 2014
We extend the Eliashberg-Thurston theorem on approximations of taut oriented $C^2$-foliations of 3-manifolds by both positive and negative contact structures to a large class of taut oriented
Foliations and the topology of 3-manifolds
In this announcement we discuss the close relationship between the topology of 3-manifolds and the foliations that is possesses. We will introduce and state the main result, then use it and the ideas
Bordered Heegaard Floer Homology and Graph Manifolds
We perform two explicit computations of bordered Heegaard Floer invariants. The first is the type D trimodule associated to the trivial S^1 bundle over the pair of pants P. The second is a bimodule