arXiv
Open Access
2020
On $1$-bridge braids, satellite knots, the manifold $v2503$ and non-left-orderable surgeries and fillings
Zipei Nie
Abstrak
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.
Topik & Kata Kunci
Penulis (1)
Z
Zipei Nie
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2020
- Bahasa
- en
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- arXiv
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- Open Access ✓