This leads to showing that all knots in some lens spaces are determined by their complements. Finally, we establish that knots of genus greater than $1$ in the Brieskorn sphere $\\Sigma(2,3,7)$ are also determined by their complements....
High-dimensional knots with are determined by their complements in one more dimension than Farber's range 来自 ResearchGate 喜欢 0 阅读量: 19 作者: W Richter 摘要: The surgery theory of Browder, Lashof, and Shaneson reduces the study of high-dimensional smooth knots with to homotopy ...
Gordon C.McA., Luecke J.: Knots are determined by their complements. J. Amer. Math. Soc. 2, 371–415 (1989) Article MathSciNet MATH Google Scholar A. Guionnet, V.F.R. Jones and D. Shlyakhtenko, Random matrices, free probability, planar algebras and subfactors, In: Quanta of Mat...
For ordinary knots K they are closely relat... E Byberi,V Chernov - 《Communications in Contemporary Mathematics》 被引量: 13发表: 2008年 Knots with unknotting number one are determined by their complements A. Thompson, Knots with unknotting number one are determined by their complements, ...
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 ...
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 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....
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...
Cappell and Shaneson gave the first examples of knots which are not determined by their complements. Their method works for each n>1, as long as certain square matrices of size n+1 exist, but such matrices have been found only for n=2, 3, 4, 5. We prove here by completely different...
The alternating knots which allow an incompressible, boundary incompressible, punctured torus to be properly imbedded in their complements are determined t... RM Patton - 《Mathematische Annalen》 被引量: 33发表: 1995年 Epimorphisms and boundary slopes of 2—bridge knots In this article we study...