Related papers: Equivariant annular Khovanov homology
The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical…
Khovanov homology is an invariant for links in the three sphere that categorizes the Jones polynomial. We extend Khovanov's construction to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces. Cutting…
We use categorical annular evaluation to give a uniform construction of both $\mathfrak{sl}_n$ and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these theories. Variations on our construction yield…
We construct explicitly the Khovanov homology theory for virtual links with arbitrary coefficients by using the twisted coefficients method. This method also works for constructing Khovanov homology for ``non-oriented virtual knots'' in the…
We prove that the Nakayama automorphism of a Frobenius algebra acts trivially on the Hochschild cohomology of the algebra. As an application of this fact, we show how to construct certain invariants attached to such algebras, and to their…
In this paper we introduce the Yokonuma-Temperley-Lieb algebra as a quotient of the Yokonuma-Hecke algebra over a two-sided ideal generated by an expression analogous to the one of the classical Temperley-Lieb algebra. The main theorem…
In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous…
We relate Kellendonk and Putnam's pattern-equivariant (PE) cohomology to the inverse-limit structure of a tiling space. This gives a version of PE cohomology with integer coefficients, or with coefficients in any Abelian group. It also…
Let $\Delta$ be a trivial knot in the three-sphere. For every finite cyclic group $G$ of odd order, we construct a $G$-equivariant Khovanov homology with coefficients in the filed $\F_{2}$. This homology is an invariant of links up to…
A discussion given to the question of extending Khovanov homology from links to embedded graphs, by using the Kauffman topological invariant of embedded graphs by associating family of links and knots to a such graph by using some local…
We extend the Framization of the Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$. We first define a natural extension of the classical Temperley-Lieb algebra to Coxeter systems of type $\mathtt{B}$ and prove that such an…
Based on the results of the second author, we define an equivariant version of Lee and Bar-Natan homology for periodic links and show that there exists an equivariant spectral sequence from the equivariant Khovanov homology to equivariant…
We continue to develop the tensor-algebra approach to knot polynomials with the goal to present the story in elementary and comprehensible form. The previously reviewed description of Khovanov cohomologies for the gauge group of rank N-1=1…
An affine monoid is an additive monoid which is cancellative, pointed and finitely generated. An affine monoid $\Lambda$ has the partial order defined by $\lambda \le \lambda + \mu$. The Frobenius complex is the order complex of an open…
We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of…
We define Calabi-Yau and periodic Frobenius algebras over arbitrary base commutative rings. We define a Hochschild analogue of Tate cohomology, and show that the "stable Hochschild cohomology" of periodic CY Frobenius algebras has a…
We give a fresh introduction to the Khovanov Homology theory for knots and links, with special emphasis on its extension to tangles, cobordisms and 2-knots. By staying within a world of topological pictures a little longer than in other…
We describe an invariant of links in the three-sphere which is closely related to Khovanov's Jones polynomial homology. Our construction replaces the symmetric algebra appearing in Khovanov's definition with an exterior algebra. The two…
The computation of Khovanov homology for tangles has significant potential applications, yet explicit computational studies remain limited. In this work, we present a method for computing the Khovanov homology of tangles via an arc…
We show that odd Khovanov homology carries an action of the super Lie algebra $\mathfrak{gl}_{1|1}$, given extra choice of markings on the link. Moreover, we show that this action arises from an action on super $\mathfrak{gl}_{2}$-foams, in…