arXiv research

New algebra pong algebra computed for knot Floer homology.

Extends Loday-Quillen-Tsygan theorem to bornological Lie algebra homology.

Homology of partition algebras matches symmetric group homology under certain conditions.

New Lie algebras from knot homology.

Floer homology connects to quiver Hecke algebras in Coulomb branches.

The paper connects Brauer algebra homology to symmetric group homology.

Witt algebra acts on Khovanov-Rozansky homology of links.

New equivariant version of Khovanov homology for annuli.

We determine the second homology group of the homological Goldman Lie algebra for an oriented surface.

Homologies of Jones and partition algebras match cyclic and symmetric groups.

New method uses algebras to speed up link Floer homology calculations.

Research connects Lie algebras to configuration space (co)homology.

Homological algebra used to study local equivalence of complex rings.

Study of Khovanov homology invariants from $U(1) imes U(1)$-equivariant algebra.

An $L_\infty$-algebra is built on symplectic manifold homology.

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these…

Maps Heegaard Floer homology to Hecke algebras for surfaces.

We give a homological interpretation of the coefficients of the Hilbert series for an algebra associated with a directed graph and its dual algebra. This allows us to obtain necessary conditions for Koszulity of such algebras in terms of homological properties of the graphs. We use our results to construct algebras wit…

We construct an algebra of non-trivial homological operations on Khovanov homology with coefficients in $\mathbb Z_2$ generated by two Bockstein operations. We use the unified Khovanov homology theory developed by the first author to lift this algebra to integral Khovanov homology. We conjecture that these two algebras…

We compute the Heegaard-Floer link homology of algebraic links in terms of the multivariate Hilbert function of the corresponding plane curve singularities. The main result of the paper identifies four homologies: (a) the Heegaard-Floer link homology of the local embedded link of the germ, (b) the lattice homology asso…

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study ass…

New homological results for bordered Floer algebras derived from hypertoric categories.

We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal.

We define a torus algebra for Heegaard Floer homology.

Paper studies homology and cohomology of Temperley-Lieb algebra TL_n(a).

Study uses superalgebra homology to classify 4D Engel-like Lie algebras.

Knot lattice homology invariant of smooth knot type in rational homology spheres.

We determine the minimal number of generators of the homological Goldman Lie algebra of a surface consisting of elements of the first homology group of the surface.

Heegaard Floer homology connects to polynomial representations of Hecke algebras.

While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied …

New algebra structure for Legendrian knots preserves contact homology invariants.

New method computes automorphisms of surface groups using skein algebras.

Knot Floer homology is a knot invariant defined using holomorphic curves. In more recent work, taking cues from bordered Floer homology,the authors described another knot invariant, called "bordered knot Floer homology", which has an explicit algebraic and combinatorial construction. In the present paper, we extend the…

Defines odd Khovanov homology via categorification of q-Schur algebra.

Researchers determined the second homology group of a specific symplectic derivation Lie algebra.

This paper upgrades Khovanov homology to an L-infinity module structure.

New spectral sequence connects link homology to Hochschild homology.

Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary …

We give a short elementary proof that a Khovanov-type link homology constructed from a diagonalisable Frobenius algebra is degenerate.

The paper explains why a specific type of link homology is useful.

We show that Khovanov homology and Hochschild homology theories share common structure. In fact they overlap: Khovanov homology of a $(2,n)$-torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete connectio…

We determine all the ideals of the homological Goldman Lie algebra, which reflects the structure of an oriented surface.

Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$-manifolds whose coefficient systems are $n$-disk algebras or $n$-disk stacks. In this work we prove a precise formulation of this idea, giving an axiomatic characterization of fa…

In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one term and two term (rack) homology theori…

New algebraic description connects Fukaya category to bordered Floer homology.

Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid of homology cylinders over S is defined by clasper surgery. Using a functorial …

In this paper we introduce a chain complex $C_{1 \pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of resolutions with differential d=d_0+d_1. We show that the E_2 page of the assoc…

This paper reinterprets Khovanov-Sano symmetries using BV formalism.