A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extend Kauffman bracket skein module to homology theory using Heegaard splittings
Proves a new skein exact triangle for real monopole Floer homology.
Grid homology theory for spatial graphs extends skein sequence.
New skein exact triangles for link Floer homology.
The paper studies splitting maps in link Floer homology using skein exact sequences.
Defines band maps in unoriented link Floer homology forming a skein exact triangle.
Skein theory aids in computing YB homology and cohomology groups.
Paper categorifies Vassiliev skein relation for Khovanov homology.
We generalize our previous work on categorification of Kauffman bracket skein module of surfaces, by extending our homology to tangles in cylinders over surfaces, F x [0,1]. Our homology of 0-tangles and 1-tangles in D^3 coincides (up to normalization) with Khovanov link homology and the reduced Khovanov link homology.…
New modules derived from Khovanov homology for links.
New invariants derived from link homology for 4-manifolds.
New skein categories for non-semisimple settings, extending existing theory.
New method computes automorphisms of surface groups using skein algebras.
Proves Khovanov homology functoriality and positivity for gl2 webs.
Given a Heegaard splitting of a closed 3-manifold, the skein modules of the two handlebodies are modules over the skein algebra of their common boundary surface. The zeroth Hochschild homology of the skein algebra of a surface with coefficients in the tensor product of the skein modules of two handlebodies is interpret…
The paper introduces a cobordism for Khovanov homology crossing change and categorifies Vassiliev skein relations.
The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are ab…
Khovanov homology distinguishes exotic 4-manifolds.
We present an easy example of mutant links with different Khovanov homology. The existence of such an example is important because it shows that Khovanov homology cannot be defined with a skein rule similar to the skein relation for the Jones polynomial.
Link homology theories connect to 4-manifold invariants and TQFTs.
In a previous paper, Vértesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle a differential graded bimodule . If is obtained by gluing together , then the knot Floer homology $\hat{\mathrm{HFK}}(L)…
New module constructs exotic surfaces in 4-manifolds.
Skein lasagna module calculates 4-manifold invariants using handle decompositions.
Study on skein module dimensions at irreducible representations.
Extends Kauffman's formula to 3-manifolds with markings.
Combinatorial proof of grid homology properties.
Explains Khovanov homology and its applications.
Researchers calculate dimensions of skein modules for 2-torus mapping tori.
New definition of skein lasagna module for specific 4-manifolds.
Grid homology properties for MOY graphs studied.
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 refinement of the Kauffman bracket skein algebra, and its categorification is constructe…
We re-derive Manolescu's unoriented skein exact triangle for knot Floer homology over F_2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, …
Khovanov homology ranks 2 for certain knots in a specific bundle.
The aim of this paper is to study the skein exact sequence for knot Floer homology. We prove precise graded version of this sequence, and also one using $\HFm$. Moreover, a complete argument is also given purely within the realm of grid diagrams.
New method computes first Vassiliev derivative of Khovanov homology.
This paper defines a spectral sequence connecting knot homologies.
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n,n) Springer variety. The results build on Khovanov's work with crossingless matchings and the cohomology of the (n,n) Springer variety. We also give a formula fo…
New spectral sequence connects Khovanov homology to real monopole Floer homology.
Frobenius extensions play a central role in the link homology theories based upon the sl(n) link variants, and each of these Frobenius extensions may be recast geometrically via a category of marked cobordisms in the manner of Bar-Natan. Here we explore a large family of such marked cobordism categories that are releva…
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach "algebra situs." When looking at the panorama of skein modules we see, past the rolling hills of homologies and homotopies, distant mountains - the Kauffman bracket skein mo…
Khovanov defined graded homology groups for links L in R^3 and showed that their polynomial Euler characteristic is the Jones polynomial of L. Khovanov's construction does not extend in a straightforward way to links in I-bundles M over surfaces F not D^2 (except for the homology with Z/2 coefficients only). Hence, the…
We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A,A^{-1}] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z_2 homology of the manifold, …
Let be a trivial knot in the three-sphere. For every finite cyclic group of odd order, we construct a -equivariant Khovanov homology with coefficients in the filed $\F_{2}$. This homology is an invariant of links up to isotopy in . Another interpretation is given using the categorification of the …
The paper calculates a new invariant for 4-manifolds using handle decompositions and skein relations.
This work extends knot homology theory to links, proving exact triangles and categorifying link signatures.
Paper computes a specific term of knot homology for 3-braids.
We describe in this chapter (Chapter IX) the idea of building an algebraic topology based on knots (or more generally on the position of embedded objects). That is, our basic building blocks are considered up to ambient isotopy (not homotopy or homology). For example, one should start from knots in 3-manifolds, surface…
We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.