3 papers
math.MG2025
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…
math.GT2025
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…
math.GT2025
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…