# Euler class of taut foliations and Dehn filling

@article{Hu2019EulerCO, title={Euler class of taut foliations and Dehn filling}, author={Ying Hu}, journal={arXiv: Geometric Topology}, year={2019} }

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 taut foliations on Dehn fillings of $X$ that are transverse to the core of the filling solid torus to vanish, from which restrictions on the range of the filling slopes are derived. Precise calculations are done for taut foliations that are carried by certain nice branched surfaces. Implications of…

## 3 Citations

### L-spaces, taut foliations and the Whitehead link

- Mathematics
- 2022

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…

### Classical pretzel knots and left orderability

- Mathematics
- 2020

We consider the classical pretzel knots $P(a_1, a_2, a_3)$, where $a_1, a_2, a_3$ are positive odd integers. By using continuous paths of elliptic $\mathrm{SL}_2(\mathbb R)$-representations, we show…

### Taut foliations, left-orders, and pseudo-Anosov mapping tori

- Mathematics
- 2020

For a large class of 3-manifolds with taut foliations, we construct an action of $\pi_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms which captures the transverse geometry of the…

## References

SHOWING 1-10 OF 73 REFERENCES

### Laminations and groups of homeomorphisms of the circle

- Mathematics
- 2003

Abstract.If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that π1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions…

### Monopoles and lens space surgeries

- Mathematics
- 2003

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a nontrivial knot in the three-sphere. To obtain this result, we use a surgery long…

### Orders

- LawUnified Patent Protection in Europe: A Commentary
- 2018

Following Rule 350, Rule 351 sets out the formal minimum requirements to be met by a judicial order outside a decision. These conditions are distinguished by whether the Court, pursuant to the…

### Taut foliations, left-orders, and pseudo-Anosov mapping tori

- Mathematics
- 2020

For a large class of 3-manifolds with taut foliations, we construct an action of $\pi_1(M)$ on $\mathbb{R}$ by orientation preserving homeomorphisms which captures the transverse geometry of the…

### Integral left-orderable surgeries on genus one fibered knots

- MathematicsJournal of Knot Theory and Its Ramifications
- 2020

Following the classification of genus one fibered knots in lens spaces by Baker, we determine hyperbolic genus one fibered knots in lens spaces on whose all integral Dehn surgeries yield closed…

### Taut foliations in punctured surface bundles, I

- Mathematics
- 2001

Given a fibred, compact, orientable 3‐manifold with single boundary component, we show that a fibration with fiber surface of negative Euler characteristic can be perturbed to yield taut foliations…

### FOLIATIONS AND THE TOPOLOGY OF 3-MANIFOLDS. II

- Mathematics
- 2008

In this paper and its continuation [3] we investigate the following question: Let M be a compact oriented irreducible 3-manifold whose boundary is a torus. If TV is obtained by filling dM along an…