activity
20202026
most citedAn algorithm for computing the -invariant and the -invariants of Dehn surgeries

1 citations · 1 across the 8 of their papers we have counts for

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math.GT2026

Involutive Khovanov homology and equivariant knots II

Taketo Sano

In the spirit of Bar-Natan's formulation of Khovanov homology for tangles, we extend the framework of involutive Khovanov homology to involutive tangles. This enables a divide-and-…

math.GT2026

A -ification of Khovanov homology

Taketo Sano

Motivated by the -ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the -action of Gorsky, Hogancamp, and Mellit, we construct -ifications of Kho…

math.GT2025

Cobordism maps in Khovanov homology and singular instanton homology II

Hayato Imori, Taketo Sano, Kouki Sato +1

This paper is a continuation of our previous work, where we defined an embedded cobordism map on the instanton cube complex that recovers the cobordism maps both in Khovanov homolo…

math.GT2025

Cobordism maps in Khovanov homology and singular instanton homology I

Hayato Imori, Taketo Sano, Kouki Sato +1

Khovanov homology and singular instanton Floer homology are both functorial with respect to link cobordisms. Although the two homology groups are related by a spectral sequence, di…

math.GT2025

A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

KeeTaek Kim, Taketo Sano

We introduce a diagrammatic approach to Rasmussen's -invariant, based on Bar-Natan's reformulation of Khovanov homology for tangles and cobordisms. This method enables a local c…

math.GT2025

On the slice-torus invariant from -equivariant Seiberg--Witten Floer cohomology

Nobuo Iida, Taketo Sano, Kouki Sato +1

We show that Iida--Taniguchi's -valued slice-torus invariant cannot be realized as a linear combination of Rasmussen's -invariant, Ozsváth--Szabó's -invaria…