7 papers · 1 filter
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-…
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…
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…
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…
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…
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 -inva…