13 citations · 23 across the 14 of their papers we have counts for
14 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 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 integra…
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…
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 -invaria…
Involutive Khovanov homology and equivariant knots
Taketo Sano
For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants , which i…
A family of slice-torus invariants from the divisibility of Lee classes
Taketo Sano, Kouki Sato
We give a family of slice-torus invariants , each defined from the -divisibility of the reduced Lee class in a variant of reduced Khovanov homology, parameterized…
Computations of HOMFLY homology
Keita Nakagane, Taketo Sano
Khovanov--Rozansky's HOMFLY homology is determined for all prime knots with up to 11 crossings by direct computations.
A Bar-Natan homotopy type
Taketo Sano
A spatial refinement of Bar-Natan homology is given, that is, for any link diagram we construct a CW-spectrum whose reduced cellular cochain comp…
Fixing the functoriality of Khovanov homology: a simple approach
Taketo Sano
Khovanov homology is functorial up to sign with respect to link cobordisms. The sign indeterminacy has been fixed by several authors, by extending the original theory both conceptu…
An algorithm for computing the -invariant and the -invariants of Dehn surgeries
Taketo Sano, Kouki Sato
By using grid homology theory, we give an explicit algorithm for computing Ozsváth-Stipsicz-Szabó's -invariant and the -invariant of Dehn surgeries along knots in . As i…
Divisibility of Lee's class and its relation with Rasmussen's invariant
Taketo Sano
Lee homology (a variant of Khovanov homology) over possesses the "canonical generators" as its basis. The generators (Lee's classes) are constructed combin…