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.
New algebra pong algebra computed for knot Floer homology.
New method uses algebras to speed up link Floer homology calculations.
Maps Heegaard Floer homology to Hecke algebras for surfaces.
Floer homology connects to quiver Hecke algebras in Coulomb branches.
Study algebraic curves in C^2 using Floer theory.
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 …
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…
Heegaard Floer homology connects to polynomial representations of Hecke algebras.
We define a torus algebra for Heegaard Floer homology.
We outline Hutchings's prescription that produces an ECH analog of Latschev and Wendl's algebraic -torsion in the context of , a variant of ECH used in a proof of the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies; and we explain how it translates into Heegaard Floer homology.
We give a partial characterization of bordered Floer homology in terms of sutured Floer homology. The bordered algebra and modules are direct sums of certain sutured Floer complexes. The algebra multiplication and algebra action correspond to a new gluing map on SFH. It is defined algebraically, and is a special case o…
Study calculates Floer homology for binary polyhedral spaces.
New algebraic description connects Fukaya category to bordered Floer homology.
New homological results for bordered Floer algebras derived from hypertoric categories.
Paper establishes an isomorphism between Fukaya category and bordered knot Floer homology.
Defines algebraic structures in Lagrangian Floer cohomology using differential forms.
Study algebraic obstructions to knot-like complex realizability.
A mathematical isomorphism connects Floer homology to DAHA representations.
If the Bing double of a knot K is slice, then K is algebraically slice. In addition, Heegaard--Floer concordance invariants developed by Ozsvath-Szabo and by Manolescu-Owens vanish on K.
Defines tensor products for A-infinity structures using diagonals.
Contact gluing maps are shown to be equivalent in sutured Floer homology.
In this paper we show how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures in Hamiltonian Floer theory. Using the SFT of Hamiltonian mapping tori we show how to define a homotopy extension of the well-known Lie bracket and discus…
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.
Study shows how knot Floer homology and bordered Floer theory are linked.
Algebraic methods prove knot primality using Floer homology.
We survey Ozsváth-Szabó's bordered approach to knot Floer homology. After a quick introduction to knot Floer homology, we introduce the relevant algebraic concepts (-modules, type -structures, box tensor, etc.), we discuss partial Kauffman states, the construction of the boundary algebra, and ske…
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…
Survey of Floer theories and their connections.
Generalizing our ideas in [arXiv:1006.3313], we explain how topologically-twisted N=2 gauge theory on a four-manifold with boundary, will allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture, (ii) Munoz's theorem relating quantum and instanton Floer cohomology, (iii) their monopole counterparts…
This paper constructs Koszul duals for Heegaard Floer Dehn surgery formulas.
In this paper we introduce a chain complex 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…
New formulas link Milnor invariants to Heegaard Floer homology.
New algebras and maps defined in knot Floer homology for trivalent vertices.
We compute the Floer homology of mapping classes which do not have any pseudo-Anosov components in the sense of Thurston's theory of surface diffeomorphisms. The formula for the Floer homology is obtained from a topological separation of fixed points and a separation mechanism for Floer connecting orbits. As examples, …
We compute the Heegaard Floer homology of an oriented 3-manifold obtained by a negative rational surgery along an arbitrary algebraic knot.
Lecture notes on Heegaard Floer homology for beginners.
Enhances knot Floer homology with algebraic representation theory.
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…
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.
It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of detects more structure of minimal genus Seifert surfaces for . We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homol…
New proof of Heegaard Floer surgery formulas using Fukaya category of the torus.
For a rational homology 3-sphere with a $\spinc$ structure $\s$, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology lead to a collection of variants which are topological invariants. We establish exact sequences relating them, we show that they satisfy a dua…
Decategorifies higher actions in Heegaard Floer homology.
Knot Floer homology is an invariant for knots discovered by the authors and, independently, Jacob Rasmussen. The discovery of this invariant grew naturally out of studying how a certain three-manifold invariant, Heegaard Floer homology, changes as the three-manifold undergoes Dehn surgery along a knot. Since its origin…
We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced Floer homology. Up to absolute grading shifts, there are only two. We use this coro…
Extends Heegaard Floer theory to surfaces of dimension one.
The main goal of this paper is to discuss a symplectic interpretation of Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of Fukaya categories of symmetric products and Lagrangian correspondences. More specifically, we give a description of the algebra A(F) which appears in the work of Lipshit…
We prove several combinatorial results on path algebras over discrete structures related to directed graphs. These results are motivated by Morse theory on a manifold with boundary and, more generally, by Floer theory on a configuration space with boundary. Their purpose is to organize cobordism relationships among mod…