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, DanielAix Marseille UnivTopology & Its Applications
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 ...
(2.17) Notice that the eigenvalues of eν are determined by the mass parameter m. Now we can specify the point PSCFT on the moduli space of vacua which is taken in the definition (2.7). First, let us consider more generally. For simplicity we assume that the moduli space of vacua on...
The moduli of the vacua in the N = 2∗ 4d U(Q) gauge theory are known to be parameterized by the U(Q) flat connections on the torus with one marked point with par- ticular holonomy determined by the deformation parameter. This is exactly the description of phase space of the ...
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 ...
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....
We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H1(L(p, q)).Ichihara, Kazuhiro...
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...
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...