4 papers · 1 filter
Purely cosmetic surgeries and Casson--Walker--Lescop invariants
Kazuhiro Ichihara, In Dae Jong, Yasuyoshi Tsutsumi
Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the -sphere, we show that any null-homologous knot in a rational homology sphere admits a…
An exploration of low crossing and chiral cosmetic bands with grid diagrams
Agnese Barbensi, Daniele Celoria, Christopher Ktenidis +3
We computationally explore non-coherent band attachments between low crossing number knots, using grid diagrams. We significantly improve the current H(2)-distance table. In partic…
Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
Kazuhiro Ichihara, In Dae Jong
We study cosmetic surgeries on a knot in a homology sphere. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredient is the rational s…
Large alternating Montesinos knots do not admit purely cosmetic surgeries
Kazuhiro Ichihara, In Dae Jong
It is conjectured that, on a non-trivial knot in the 3-sphere, no pair of Dehn surgeries along distinct slopes are purely cosmetic, that is, none of them yield 3-manifolds those ar…