8 papers
Purely cosmetic surgeries on knots with low-span Jones polynomials, II
Kazuhiro Ichihara, Kengo Kishimoto
We show that a knot in the 3-sphere with a nontrivial Jones polynomial of span at most 14 admits no purely cosmetic surgery. This extends a result of the first author for span at m…
Purely cosmetic surgeries on knots with low-span Jones polynomials
Kazuhiro Ichihara
In this paper, we show that a knot with a nontrivial Jones polynomial of span at most 11 does not admit purely cosmetic surgery.
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…
Theorem of three squares across three geometries
Kazuhiro Ichihara, Akira Ushijima
In Euclidean geometry, the Pythagorean theorem is presented as an equation involving three squares. This paper explores how analogous expressions may be identified in spherical and…
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…
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…
Exceptional or half-integral chirally cosmetic surgeries
Kazuhiro Ichihara, Toshio Saito
A pair of Dehn surgeries on a knot is called chirally cosmetic if they yield orientation-reversingly homeomorphic 3-manifolds. In this paper, we consider exceptional or half-integr…
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…