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 method computes knot Floer homology for satellite knots.
Lecture notes on Heegaard Floer homology for 3-manifolds and knots.
In this survey article, we discuss several different knot concordance invariants coming from the Heegaard Floer homology package of Ozsvath and Szabo. Along the way, we prove that if two knots are concordant, then their knot Floer complexes satisfy a certain type of stable equivalence.
Study of knot Floer homology and its relation to Heegaard Floer homology via equivariant surgery.
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…
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to -equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, and …
Formula for satellite operators using knot Floer homology.
Formula for Heegaard Floer multicurves of double tangles from knot complements.
Study on knot concordance and homology cobordism using Heegaard Floer homology.
Paper classifies Heegaard Floer minimal knots in sutured manifolds.
Defines a new Upsilon torsion function for knot Floer homology.
Proves properties of instanton knot Floer homology and connected sum formula.
New invariants improve Heegaard Floer slice genus and clasp number bounds.
Real Heegaard Floer Homology extends Li's real monopole Floer homology.
Paper classifies type of almost L-space knots.
New Heegaard Floer homology findings block chirally cosmetic surgeries.
We give a precise description of splicing formulas from a previous paper in terms of knot Floer complex associated with a knot in homology sphere.
Study proves naturality and functoriality in a type of Heegaard Floer homology.
Unified model for knot polynomials using quantum Heegaard diagrams.
Determine pairs of torus knots with genus one cobordisms, with exceptions.
We compute the Ozsváth-Szabó Heegaard Floer homology of three stranded pretzel knots.
The paper reconfirms a lower bound on rational genus using Heegaard Floer homology.
Combinatorial method computes Legendrian knot invariant.
New technique connects instanton Floer homology to Heegaard diagrams for knots and 3-manifolds.
Research shows Khovanov homology can identify split links.
New insights into cosmetic surgeries using Heegaard Floer homology.
Characterizes knots with large Dehn surgeries.
We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus two mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus two mutant by both knot Floer hom…
Tests using knot Floer homology detect prime knots with high accuracy.
Floer homology detects right-veering monodromy in fibered knots.
In this brief note, we give an explicit sequence of Heegaard moves interpolating between local versions of the Kauffman-states Heegaard diagram and the planar Heegaard diagram used in knot Floer homology, and show how these local moves can be used to go between the global versions of the Heegaard diagrams.
We show that if K is a non-trivial knot inside a homology sphere Y, then the rank of knot Floer homology associated with K is strictly bigger than the rank of Heegaard Floer homology of Y.
We use bordered Heegaard Floer homology to compute the tau invariant of a family of satellite knots obtained via twisted infection along two components of the Borromean rings, a generalization of Whitehead doubling. We show that tau of the resulting knot depends only on the two twisting parameters and the values of tau…
Surgery on knots can produce non-separating spheres, using Heegaard Floer homology.
Study shows link polynomial evaluations from Heegaard Floer theory.
Real Heegaard Floer homology gets a new grading for certain 3-manifolds.
New proof of Heegaard Floer surgery formulas using Fukaya category of the torus.
Researchers link knot Floer homology, Burau representation, and quantum gl(1|1).
New knots not slice in rational 4-balls found.
Study exact surgery formula in involutive Heegaard Floer homology.
In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y, which is closely related to the Heegaard Floer homology of Y. In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description fo…
Study surgeries on Klein bottle knots in 3-manifolds using Heegaard Floer homology.
Let be a null-homologous knot in a three-manifold . We give a description of the Heegaard Floer homology of integer surgeries on along in terms of the filtered homotopy type of the knot invariant for . As an illustration, we calculate the Heegaard Floer homology groups of non-trivial circle bundles ov…
We define sutured Heegaard diagrams for null-homologous knots in 3-manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum. Our result echoes Gabai's earlier works. We also show that for so…
In 2003, Ozsváth and Szabó defined the concordance invariant for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of for knots in and a combinatorial proof that gives a lower bound for the slice genus of a knot. Recently, Har…
Given a diagram of a link K in S^3, we write down a Heegaard diagram for the branched-double cover Sigma(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model we make some computations of the homology \hat{HF}(Sigma(K)) as a graded group. W…
Using the combinatorial approach to Heegaard Floer homology we obtain a relatively easy formula for computation of hat Heegaard Floer homology for the three-manifold obtained by rational surgery on a knot K inside a homology sphere Y.
We compute the knot Floer filtration induced by a cable of the meridian of a knot in the manifold obtained by large integer surgery along the knot. We give a formula in terms of the original knot Floer complex of the knot in the three-sphere. As an application, we show that a knot concordance invariant of Hom can equiv…