On 111-bridge braids, satellite knots, the manifold v2503v2503v2503 and non-left-orderable surgeries and fillings (original) (raw)

We define the property (D) for nontrivial knots. We show that the fundamental group of the manifold obtained by Dehn surgery on a knot KKK with property (D) with slope fracpqge2g(K)−1\frac{p}{q}\ge 2g(K)-1fracpqge2g(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 111-bridge braids have property (D); (2) L-space satellite knots, with positive 111-bridge braid patterns, and companion with property (D), have property (D); (3) the fundamental group of the manifold obtained by Dehn filling on v2503v2503v2503 is not left orderable. Additionally, we prove that L-space twisted torus knots of form Tp,kppm1l,mT_{p,kp\pm 1}^{l,m}Tp,kppm1l,m are closures of positive 111-bridge braids.