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.
Unified model for knot polynomials using quantum Heegaard diagrams.
New invariant from quantum algebra for 3-manifold bundles.
Researchers prove quantum invariants remain hard even when restricted.
This note explains how to transform Heegaard diagrams into framed link diagrams.
Heegaard diagrams for 5-manifolds help in understanding their structure.
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.
Study shows genus two Heegaard diagrams for all Thurston geometries.
Sutured instanton homology uses Heegaard diagrams to bound homology dimensions.
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
New method computes knot Floer homology for satellite knots.
The paper explores algorithms to transform 3-manifold triangulations while controlling sparsity.
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
Lecture notes on Heegaard Floer homology for 3-manifolds and knots.
Formula for computing triple-cup product from Heegaard diagrams of 3-manifolds.
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…
We describe a correspondence between Turaev surfaces of link diagrams on and special Heegaard diagrams for adapted to links.
We review the use of grid diagrams in the development of Heegaard Floer theory. We describe the construction of the combinatorial link Floer complex, and the resulting algorithm for unknot detection. We also explain how grid diagrams can be used to show that the Heegaard Floer invariants of 3-manifolds and 4-manifolds …
Polynomials derived from Heegaard diagrams for 3-manifolds.
We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings o…
We show that the Andrews-Curtis conjecture holds for all balanced presentations of the trivial group corresponding to Heegaard diagrams of .
The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construct…
Constructs Koszul dual algebras for star-shaped diagrams in 3-manifolds.
A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the -fold symmetric product of the Heegaard surface. This leads to a topological invariant for three-manifolds, Heegaard Floer homology, which is functorial under cobo…
New criteria for Heegaard splittings ensure strong irreducibility and finite Goeritz groups.
We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.
Algorithm constructs Kirby diagrams for 4D open books.
Topological model created for HOMFLY-PT polynomial from link diagrams.
The paper constructs trisections for fiber bundles over a circle.
We prove a 20-year-old conjecture concerning two quantum invariants of three manifolds that are constructed from finite dimensional Hopf algebras, namely, the Kuperberg invariant and the Hennings-Kauffman-Radford invariant. The two invariants can be viewed as a non-semisimple generalization of the Turaev-Viro-Barrett-W…
Proves a formula in Heegaard Floer homology using combinatorial methods.
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…
The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard dia…
We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that every strong L-space is the branched double cover of an alternating link in the t…
We give a parity condition of a Heegaard diagram to show that it is unstabilized. This improves the result of [5]. As an application, we construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.
Multisections generalize Heegaard splittings and trisections to higher dimensions.
We give combinatorial descriptions of the Heegaard Floer homology groups for arbitrary three-manifolds (with coefficients in Z/2). The descriptions are based on presenting the three-manifold as an integer surgery on a link in the three-sphere, and then using a grid diagram for the link. We also give combinatorial descr…
Programs compute Heegaard Floer invariants from open books.
Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsvath-Szabo invariant is com…
The paper connects quantum invariants to intersections of Lagrangians in symmetric power spaces.
The paper studies Morse flows on 3-manifold boundaries with fixed points.
Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.
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…
The paper constructs quantum invariants for knotoid diagrams.
We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show…
We consider a stabilized version of hat Heegaard Floer homology of a 3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed 3-manifolds). We give a combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a combinatorial proof of its invariance pr…
Data structure for Heegaard splittings reduces complexity.
New technique connects instanton Floer homology to Heegaard diagrams for knots and 3-manifolds.
We describe some of the algebra underlying the decomposition of planar grid diagrams. This provides a useful toy model for an extension of Heegaard Floer homology to 3-manifolds with parametrized boundary. This paper is meant to serve as a gentle introduction to the subject, and does not itself have immediate topologic…