On $1$-bridge braids, satellite knots, the manifold $v2503$ and non-left-orderable surgeries and fillings

Abstract

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 left orderable. By making full use of the fixed point method, we prove that (1) nontrivial knots which are closures of positive $1$-bridge braids have property (D); (2) L-space satellite knots, with positive $1$-bridge braid patterns, and companion with property (D), have property (D); (3) the fundamental group of the manifold obtained by Dehn filling on $v2503$ is not left orderable. Additionally, we prove that L-space twisted torus knots of form $T_{p,kp\pm 1}^{l,m}$ are closures of positive $1$-bridge braids.

17 pages

References in corpus (4)

• Slope detection, foliations in graph manifolds, and L-spaces
• An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery
• Non-Left-Orderable Surgeries on 1-Bridge Braids
• A Note on the Orderability of Dehn Fillings of the Manifold $v2503$

Cited by in corpus (1)

• An explicit description of $(1,1)$ L-space knots, and non-left-orderable surgeries