Related papers: A Diagramless Link Homology
We revisit Rozansky's construction of Khovanov homology for links in $S^2\times S^1$, extending it to define Khovanov homology $Kh(L)$ for links $L$ in $M^r=#^r(S^2\times S^1)$ for any $r$. The graded Euler characteristic of $Kh(L)$ can be…
A categorification of a polynomial link invariant is an homological invariant which contains the polynomial one as its graded Euler characteristic. This field has been initiated by Khovanov categorification of the Jones polynomial. Later,…
Let $V$ be a closed 3-manifold with a contact form $\lambda$, and let $L$ be a link consisting of closed orbits for the Reeb vector field of $\lambda$. We study the problem of defining cylindrical contact homology on the non-compact…
We define for every dendroidal set X a chain complex and show that this assignment determines a left Quillen functor. Then we define the homology groups $H_n(X)$ as the homology groups of this chain complex. This generalizes the homology of…
A graph multilink is a link with multiplicities in a homology 3-sphere whose exterior is a graph manifold. In this Note, we compute the Novikov homology of graph multilinks. As a corollary, we give a majoration for the number of Novikov…
Inspired by bordered Floer homology, we describe a type A structure on a Khovanov homology for a tangle, which complements the type D structure in a previous paper. The type A structure is a differential module over a certain algebra. This…
We define and study a family of link invariants $\mathit{HFK}_{n}(L)$. Although these homology theories are defined using holomorphic disc counts, they share many properties with $sl_{n}$ homology. Using these theories, we give a framework…
Recently N.A'Campo suggested a construction of a link from a generic immersion of a curve into a 2-disk. It is tightly related to the singularity theory. In this paper, we give a simple procedure to draw a diagram of the link from a picture…
One deals with arbitrary reduced free divisors in a polynomial ring over a field of characteristic zero, by stressing the ideal theoretic and homological behavior of the corresponding singular locus. A particular emphasis is given to both…
This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives criteria under which the homology of a diagram algebra is isomorphic to the homology of the subalgebra on diagrams having the…
We exhibit pairs of transverse knots with the same self-linking number that are not transversely isotopic, using the recently defined knot Floer homology invariant for transverse knots and some algebraic refinements of it.
We develop some basic homological theory of hopfological algebra as defined by Khovanov. Several homological properties in hopfological algebra analogous to those of usual homological theory of DG algebras are obtained.
We prove that the length of any gap in the differential grading of the Khovanov homology of any quasi-alternating link is one. As a consequence, we obtain that the length of any gap in the Jones polynomial of any such link is one. This…
The Blanchet link homology theory is an oriented model of Khovanov homology, functorial over the integers with respect to link cobordisms. We formulate a stable homotopy refinement of the Blanchet theory, based on a comparison of the…
We define link and graph invariants from entropic magmas modeling them on the Kauffman bracket and Tutte polynomial. We define the homology of entropic magmas. We also consider groups that can be assigned to the families of compatible…
Using the symplectic geometry of certain manifolds which appear naturally in Lie theory, we define an invariant which assigns a graded abelian group to an oriented link. The relevant manifolds are transverse slices to certain nilpotent…
In their recent preprint, Baldwin, Ozsv\'{a}th and Szab\'{o} defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsv\'{a}th and Szab\'{o}, from Khovanov homology to Heegaard-Floer…
We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.
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…
We study the space of link maps, which are smooth maps from the disjoint union of manifolds P and Q to a manifold N such that the images of P and Q are disjoint. We give a range of dimensions, interpreted as the connectivity of a certain…