By finding a different bound on the number of slopes, we show that non-null-homologous knots in certain homology $\\mathbb{R}\\mkern-2mu P^3$ are determined by their complements. We also prove the surgery characterisation of the unknot for null-homologous knots in $L$--spaces. This ...
Knots with unknotting number one are determined by their complements 1989, Topology Genus is superadditive under band connected sum 1987, Topology Band-sums are ribbon concordant to the connected sum 1998, Proceedings of the American Mathematical Society Sutured manifolds and generalized Thurston norms ...
Here, the goal is to see that hyperbolic H -knots are not determined by their complements, i.e. there is no automorphism onto the complement which sends the meridian slope to the r -slope.doi:10.1016/j.topol.2017.06.017Matignon, Daniel...
We consider the problem of whether knots in a closed 3-manifold are determined by their complements or not. The main result determines all knots whose complements are Seifert fibered spaces, with the property that the unoriented knot complements do not determine the knot types. We also describe...
The alternating knots which allow an incompressible, boundary incompressible, punctured torus to be properly imbedded in their complements are determined to be the 2-bridge knots which have a continued fraction expansion of length two and the pretzel knots. All of the incompressible tori can be ...
We obtain further that Seifert fibered knots, except for the axes, and satellite knots are determined by their complements in lens spaces. An easy application shows that non-hyperbolic knots are determined by their complement in atoroidal and irreducible Seifert fibered 3-manifolds....
A. Thompson, Knots with unknotting number one are determined by their complements, Topology 28 (1989), 225-230.A. Thompson, Knots with unknotting number one are determined by their complements., Topology vol. 28 (1989) 225-230. MR 90f:57011...