Related papers: A geometric spectral sequence in Khovanov homology
We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.
The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of one dimensional projective space with coefficients in the…
This paper is a short introduction to the combinatorial version of tangle Floer homology defined in "Combinatorial tangle Floer homology". There are two equivalent definitions---one in terms of strand diagrams, and one in terms of bordered…
We define a motivic Greenlees spectral sequence by characterising an associated $t$-structure. We then examine a motivic version of topological Hochschild homology for the motivic cohomology spectrum modulo a prime number $p$. Finally, we…
We count pseudoholomorphic curves in the higher-dimensional Heegaard Floer homology of disjoint cotangent fibers of a two dimensional disk. We show that the resulting algebra is isomorphic to the Hecke algebra associated to the symmetric…
Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B, in S^3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer…
We prove that any link in $S^3$ whose Khovanov homology is the same as that of a Hopf link must be isotopic to that Hopf link. This holds for both reduced and unreduced Khovanov homology, and with coefficients in either $\mathbb{Z}$ or…
We describe the construction of an $\mathcal{A}_\infty$ multi-module in terms of counts of holomorphic polygons in a series Heegaard multi-diagrams. We show that this is quasi-isomorphic to the type-A bordered-sutured invariant of a link…
We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild…
By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord…
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 generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give…
We construct connections on $S^1$-equivariant Hamiltonian Floer cohomology, which differentiate with respect to certain formal parameters.
Let $\Tt$ be an aperiodic and repetitive tiling of $\RM^d$ with finite local complexity. We present a spectral sequence that converges to the $K$-theory of $\Tt$ with $E_2$-page given by a new cohomology that will be called PV in reference…
For every oriented surface of finite type, we construct a functorial Khovanov homology for links in a thickening of the surface, which takes values in a categorification of the corresponding gl(2) skein module. The latter is a mild…
In this paper, we construct and study a Serre-type spectral sequence for motivic cohomology associated to a map of bisimplicial schemes with motivically cellular fiber. Then, we show how to apply it in order to approach the computation of…
In earlier work of the authors, the Khovanov complex of a knot or link appeared as the first page in a spectral sequence abutting to the instanton homology. The quantum and (co)homological gradings on Khovanov homology do not survive as…
In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and…
By considering a version of Khovanov homology incorporating both the Lee and $E(-1)$ differentials, we construct a $1$-parameter family of concordance homomorphisms similar to the Upsilon invariant from knot Floer homology. This invariant…
We construct the concordance invariant coming from the $E(-1)$ spectral sequence on Khovanov homology in the same way Rasmussen's $s$ invariant comes from the Lee spectral sequence, and show that it gives a bound on the nonorientable slice…