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math.AG2025
The border rank of the determinant tensor is twelve
Jong In Han, Jeong-Hoon Ju, Yeongrak Kim
We show that the border rank of the determinant tensor is at least over , using the fixed ideal theorem introduced by Buczyńska-Buczyński and the meth…
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…