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}
}
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. 
L-spaces, taut foliations and the Whitehead link
We prove that if M is a rational homology sphere that is a Dehn surgery on the Whitehead link, then M is not an L-space if and only if M supports a coorientable taut foliation. The left orderability
Floer homology, group orderability, and taut foliations of hyperbolic 3–manifolds
This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and
Euler class of taut foliations and Dehn filling
We study the Euler class of co-orientable taut foliations on rational homology spheres. Given a rational homology solid torus $X$, we give necessary and sufficient conditions for the Euler class of
The equivalence of lattice and Heegaard Floer homology
We prove that if Y is a 3-manifold which is the boundary of a plumbing of a tree of disk bundles over S, then the lattice homology of Y coincides with the Heegaard Floer homology of Y . We also give
Floer homology and covering spaces
We prove a Smith-type inequality for regular covering spaces in monopole Floer homology. Using the monopole Floer / Heegaard Floer correspondence, we deduce that if a 3-manifold Y admits a
Thin links and Conway spheres
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal δ-grading. This leads to the broader class of thin links that one would like to
Orderability and Dehn filling
Motivated by conjectures relating group orderability, Floer homology, and taut foliations, we discuss a systematic and broadly applicable technique for constructing left-orders on the fundamental
On the set of L-space surgeries for links
Slope detection and toroidal 3-manifolds
We investigate the L-space conjecture for toroidal 3-manifolds using various notions of slope detection. This leads to a proof that toroidal 3-manifolds with small order first homology have
...
...

References

SHOWING 1-10 OF 42 REFERENCES
Slope detection, foliations in graph manifolds, and L-spaces
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
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
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
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
...
...