8 papers
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…
Symmetries of equivariant Khovanov homology
Mikhail Khovanov, Taketo Sano
We study symmetries in equivariant versions of Khovanov homology, which include (i) the construction of an involution for the -equivariant theory, (ii) an integr…
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…