arXiv research

Researchers link tangle invariants for Khovanov and knot Floer homologies.

New formal groupoid scheme emerges from Lie algebroid sections.

Foams 2-equivalent to singular Soergel bimodules.

New algebras and maps defined in knot Floer homology for trivalent vertices.

Paper proposes BSP to find stable bimodules of cross-correlated features.

We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.

Study links using Soergel bimodules and Serre duality.

The paper solves a problem in constructing a bicategory of algebra bundles.

Study categorifies link invariants using Soergel bimodules.

New invariant for links in handlebodies defined using braid groups and Soergel bimodules.

Decomposes Goldman-Turaev Lie bialgebra via cutting a surface.

We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associated to the double-branched cover of a braid and show that its associated graded bimodule is equivalent to a similar bimodule define…

Defines new Heegaard Floer invariants with actions of both E and F.

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

Study connects bordered theory to Khovanov-Seidel quiver algebras.

We trade matrix factorizations and Koszul complexes for Hochschild homology of Soergel bimodules to modify the construction of triply-graded link homology and relate it to Kazhdan-Lusztig theory.

New 4-manifold invariant defined from trisection diagrams.

New connections found for quantum flag manifolds modules.

New stable homotopy refinement of quantum annular Khovanov homology.

Paper proves Koszul duality for weighted A-infinity algebras.

Given a link in the three-sphere, Z. Szabó and the second author constructed a spectral sequence starting at the Khovanov homology of the link and converging to the Heegaard Floer homology of its branched double-cover. The aim of this paper and its sequel is to explicitly calculate this spectral sequence, using bordere…

Researchers define new algebraic structures for knot Floer homology.

Categorifies a skein relation for links colored by one-column Young diagrams.

Proves Serre duality in Khovanov-Rozansky homology.

Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In this paper, we establish naturality properties of this invariant. Changing the diffeomorphism between F and the boundary of Y te…

Defines state sum models with defects in 3-manifolds.

The paper proves unique Levi-Civita connections on noncommutative forms.

Spectral sequence connects knot homologies via algebraic geometry.

We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a noncommutative generalization of linear connections. We also discuss the differe…

Categorifies Hecke algebra subalgebra using sheaves and bimodules.

Authors conjecture categorically diagonalizable complex for full twists.

New categories from TQFTs interpret skein relations.

We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain $U_q(gl(1|1))$ representations. Under this identification, up to a scalar factor, the map on the Grothendieck group induced by the tangle Floer dg bimodule associated to a tangle agrees with the Reshetikhin-Turaev homomor…

Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these b…

We find a new algebra isomorphic to Khovanov's arc algebra in characteristic 2.

Study reveals striking uniformity in triply graded link homology for specific braids.

This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an example we can obtain enveloping algebra like relations for Hopf algebras with di…

Categorifies symmetric link invariants using foam technology.

We characterize the derivation $d:A\to Ω^1_{\der}(A)$ by a universal property introducing a new class of bimodules.

Minimal complexes for two-strand braids defined directly.

Classifies two-dimensional extended homotopy field theories with aspherical targets.

The Morse complex is shown to be an infinite functor.

Spinor bundle constructed on loop space for string manifolds.

This paper realises the Khovanov homology of a link in the 3-sphere as a Lagrangian Floer cohomology group, establishing a conjecture of Seidel and the second author. The starting point is the previously established formality theorem for the symplectic arc algebra over a field k of characteristic zero. Here we prove th…

Researchers create functors to match colored homologies of knots and links.

Researchers prove skein relations for tangle Floer homology.

New spectral sequence connects link homology to Hochschild homology.

Analogous exponential map defined for Hopf algebras.