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.
Lecture notes on Heegaard Floer homology for 3-manifolds and knots.
Study flippable Heegaard splittings in Seifert fibered spaces.
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
Proves a formula in Heegaard Floer homology using combinatorial methods.
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
Heegaard Floer homology study confirms composition maps match up to homotopy.
Study on equivariant Heegaard genus of reducible 3-manifolds with group actions.
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 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…
We show that if a closed hyperbolic 3-manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, we can replace the assumption that the covers have bounded Heega…
This note explains how to transform Heegaard diagrams into framed link diagrams.
Identifies Heegaard Floer homology solid tori via Dehn fillings.
Finite mapping class groups for Heegaard splittings with distance ≥ 3, but not for distance 2.
Introduces integer-valued Heegaard Floer theory with canonical orientations.
Study shows genus two Heegaard diagrams for all Thurston geometries.
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.
Heegaard diagrams for 5-manifolds help in understanding their structure.
Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a special case, we obtain critical Heegaard surfaces by boundary stabilization. It …
We expect manifolds obtained by Dehn filling to inherit properties from the knot manifold. To what extent does that hold true for the Heegaard structure? We study four changes to the Heegaard structure that may occur after filling: (1) Heegaard genus decreases, (2) a new Heegaard surface is created, (3) a non-stabilize…
Extends Khovanov homology spectral sequence using Heegaard Floer homology.
Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of non-stabilized Heegaard splittings by doing a single Dehn twist.
Extend Kauffman bracket skein module to homology theory using Heegaard splittings
Study on knot concordance and homology cobordism using Heegaard Floer homology.
We show that the standard minimal genus Heegaard splitting of (closed orientable surface)\times S^1 is a critical Heegaard splitting.
Sutured instanton homology uses Heegaard diagrams to bound homology dimensions.
A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditi…
New Heegaard Floer homology for orbifolds with cyclic singularities.
Lecture notes on Heegaard Floer homology for beginners.
Unified model for knot polynomials using quantum Heegaard diagrams.
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…
New proof of Giroux Correspondence for tight contact 3-manifolds.
Study proves naturality and functoriality in a type of Heegaard Floer homology.
We show that {\sc Heegaard Genus }, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to , is NP-hard. The result follows from a quadratic time reduction of the NP-complete problem {\sc CNF-SAT} to {\sc Heegaard Genus }.
Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces and incompressible …
New bounds on Heegaard distance for link complements in 3D space.
From the view of Heegaard splitting, it is known that if a closed orientable 3-manifold admits a distance at least three Heegaard splitting, then it is hyperbolic. However, for a closed orientable 3-manifold admitting only distance at most two Heegaard splittings, there are examples shows that it could be reducible, Se…
New signs and gradings enable detailed comparison in Heegaard Floer theory.
We show that if a Heegaard splitting is the result of stabilizing a high distance Heegaard splitting exactly once then its mapping class group is finitely generated.
Polynomials derived from Heegaard diagrams for 3-manifolds.
Let M be a closed orientable 3-manifold with a negatively curved Riemannian metric. Let {M_i} be a collection of finite regular covers with degree d_i. (1) If the Heegaard genus of M_i grows more slowly than the square root of d_i, then M_i has positive first Betti number for all sufficiently large i. (2) The strong He…
New findings restrict Heegaard Floer homology for certain rational homology spheres.
3-manifolds with Heegaard 2 admit taut foliations if their fundamental group is left-orderable.
Formula for Heegaard Floer multicurves of double tangles from knot complements.
We prove a rigidity theorem for degree one maps between small 3-manifolds using Heegaard genus, and provide some applications and connections to Heegaard genus and Dehn surgery problems.
Algorithm constructs reducing spheres for genus-2 Heegaard splitting of S^3.
The paper defines a condition for the finiteness of mapping class groups of Heegaard splittings.
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…
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…