# 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} }

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 $s$.

#### 9 Citations

Left-orderability for surgeries on twisted torus knots

- MathematicsProceedings 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

- Mathematics
- 2019

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

- Mathematics
- 2021

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

- Mathematics
- 2020

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

- Mathematics
- 2018

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

- Mathematics
- 2021

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

- MathematicsProceedings of the American Mathematical Society
- 2019

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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…

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