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.
Paper proves Koszul duality for weighted A-infinity algebras.
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.
Define web algebras for annular SL(2) and SL(3) using foam TQFTs.
Study links using Soergel bimodules and Serre duality.
The paper solves a problem in constructing a bicategory of algebra bundles.
Decomposes Goldman-Turaev Lie bialgebra via cutting a surface.
Constructs Koszul dual algebras for star-shaped diagrams in 3-manifolds.
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…
Ozsvath and Szabo recently constructed an algebraically defined invariant of tangles which takes the form of a DA bimodule. This invariant is expected to compute knot Floer homology. The authors have a similar construction for open braids and their plat closures which can be viewed as a filtered DA bimodule over the sa…
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.
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.
Recently, Ozsváth and Szabó introduced some algebraic constructions computing knot Floer homology in the spirit of bordered Floer homology, including a family of algebras B(n) and, for a generator of the braid group on n strands, a certain type of bimodule over B(n). We define analogous bimodules for singular crossings…
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.
We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived …
We investigate a relationship between Ozsváth and Szabó's bordered theory and the algebras and bimodules constructed by Khovanov-Seidel. Specifically, we show that (a variant of) a special case of Ozsváth-Szabó's algebras has a quotient which is isomorphic to the Khovanov-Seidel quiver algebra with coefficients in $\ma…
Categorifies a skein relation for links colored by one-column Young diagrams.
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…
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFLYPT (co)homology of links in the 3-ball. Our main tools are the description of these links in terms of a subgroup of the classical braid group, and a family of categorical actions built from complexes of (singular) Soerg…
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…
New categories from TQFTs interpret skein relations.
We identify the Grothendieck group of the tangle Floer dg algebra with a tensor product of certain 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 give another definition of two-dimensional extended homotopy field theories (E-HFTs) with aspherical targets and classify them. When the target of E-HFT is chosen to be a -space, we classify E-HFTs taking values in the symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by certain Frobeni…
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…
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.
We compare two different types of mapping class invariants: the Hochschild homology of an bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their Hochschild homology in the genus two case. We then compare the resulting comput…
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.
New spectral sequence connects link homology to Hochschild homology.
Analogous exponential map defined for Hopf algebras.
Enhances knot Floer homology with algebraic representation theory.
We define virtual braid groups of type B and construct a morphism from such a group to the group of isomorphism classes of some invertible complexes of bimodules up to homotopy.
Using the diagrammatic calculus for Soergel bimodules, developed by B. Elias and M. Khovanov, as well as Rasmussen's spectral sequence, we construct an integral version of HOMFLY-PT and sl(n)-link homology.
Given a link in the three-sphere, Ozsváth and Szabó showed that there is 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 is to explicitly calculate this spectral sequence in terms of bordered Floer homolo…