# Left-orderablity for surgeries on (−2,3,2s + 1)-pretzel knots

@article{Nie2019LeftorderablityFS,
title={Left-orderablity for surgeries on (−2,3,2s + 1)-pretzel knots},
author={Zipei Nie},
journal={Topology and its Applications},
year={2019}
}
• Zipei Nie
• Published 28 February 2018
• Mathematics
• Topology and its Applications
In this paper, we prove that the fundamental group of the manifold obtained by Dehn surgery along a $(-2,3,2s+1)$-pretzel knot ($s\ge 3$) with slope $\frac{p}{q}$ is not left orderable if $\frac{p}{q}\ge 2s+3$, and that it is left orderable if $\frac{p}{q}$ is in a neighborhood of zero depending on $s$.
Left-orderability for surgeries on twisted torus knots
• Anh T. Tran
• Mathematics
Proceedings of the Japan Academy, Series A, Mathematical Sciences
• 2019
We show that the fundamental group of the $3$-manifold obtained by $\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m \ge 1$, is not left-orderable if $\frac{p}{q} \ge Representations of the (-2,3,7)-pretzel knot and orderability of Dehn surgeries We construct a 1-parameter family of$\mathrm{SL}_2(\mathbf{R})$representations of the pretzel knot$P(-2,3,7)$. As a consequence, we conclude that Dehn surgeries on this knot are left-orderable for Left orderability for surgeries on the$[1,1,2,2,2j]$two-bridge knots Let M be a Q-homology solid torus. In this paper, we give a cohomological criterion for the existence of an interval of left-orderable Dehn surgeries on M . We apply this criterion to prove that the On$1$-bridge braids, satellite knots, the manifold$v2503$and non-left-orderable surgeries and fillings We define the property (D) for nontrivial knots. We show that the fundamental group of the manifold obtained by Dehn surgery on a knot$K$with property (D) with slope$\frac{p}{q}\ge 2g(K)-1$is not Taut foliations, positive 3‐braids, and the L‐space conjecture We construct taut foliations in every closed 3-manifold obtained by$r$-framed Dehn surgery along a positive 3-braid knot$K$in$S^3$, where$r < 2g(K)-1$and$g(K)$denotes the Seifert genus of An explicit description of$(1,1)$L-space knots, and non-left-orderable surgeries Greene, Lewallen and Vafaee characterized (1, 1) L-space knots in S and lens space in the notation of coherent reduced (1, 1)-diagrams. We analyze these diagrams, and deduce an explicit description Promoting circular-orderability to left-orderability • Mathematics • 2019 Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group$G\$ is
Non-left-orderable surgeries on L-space twisted torus knots
• Anh T. Tran
• Mathematics
Proceedings of the American Mathematical Society
• 2019
<p>We show that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation
Integral left-orderable surgeries on genus one fibered knots
• Mathematics
Journal 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

#### References

SHOWING 1-10 OF 32 REFERENCES
A GOOD PRESENTATION OF (-2, 3, 2s + 1)-TYPE PRETZEL KNOT GROUP AND ℝ-COVERED FOLIATION
Let Ks be a (-2, 3, 2s + 1)-type pretzel knot (s ≧ 3) and EKs(p/q) be a closed manifold obtained by Dehn surgery along Ks with a slope p/q. We prove that if q > 0, p/q ≧ 4s + 7 and p is odd, then
(-2,3,7)-pretzel knot and Reebless foliation
We show that if p/q>18, p is odd, and p/q≠37/2, then (p,q)-Dehn surgery for the (−2,3,7)-pretzel knot produces a 3-manifold without Reebless foliation. We also show that the manifold obtained by
Orderability and Dehn filling
• Mathematics
• 2016
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 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
Left-orderable fundamental groups and Dehn surgery
• Mathematics
• 2010
There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive;
Knot Floer homology and rational surgeries
• Mathematics
• 2010
Let K be a rationally null-homologous knot in a three-manifold Y . We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold
FOLIATIONS AND THE TOPOLOGY OF 3-MANIFOLDS. II
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
Boundary slopes for Montesinos knots
• Mathematics
• 1989
FOR A KNOT K c S3, let S(K) c Q u {CQ} be the set of slopes of boundary curves of incompressible, %incompressible orientable surfaces in the knot exterior, slopes being normalized in the standard way
Montesinos knots, Hopf plumbings, and L-space surgeries
• Mathematics
• 2014
Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have
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