Graph manifold L-space intervals computed and applied to cables.
problem Computing L-space intervals for graph manifolds and their cables.
method Graph manifold analog of Jankins-Neumann classification, Floer simple manifolds generalization.
result Finite recursive formula for L-space intervals of graph manifolds and cable knots.
An oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-space filling, or an interval of L-space fillings. In the latter case, which we call "Floer simple," we construct an invariant which computes the interval of L-space filling slopes from the Turaev torsion and a given slope …
Dehn filling on v2503 creates non-orderable spaces.
problem Understanding the orderability of Dehn fillings of a specific manifold.
method Analyzing rational slopes in the interval (−∞,−1) for v2503. result All fillings result in non-orderable spaces for slopes in (−∞,−1). New knots share same Upsilon invariant despite different Alexander polynomials.
problem Identifying concordant knots via Upsilon invariant.
method Examined hyperbolic L-space knots and their Upsilon invariants.
result Infinitely many pairs of hyperbolic L-space knots with distinct Alexander polynomials share the same Upsilon invariant.
Proves left-orderability of certain Dehn fillings on 3-manifolds.
problem Left-orderability of Dehn fillings on 3-manifolds.
method Constructing arcs of representations and using holonomy extension techniques.
result Establishes intervals of orderable Dehn fillings for odd pretzel knots.
An L-space is a rational homology 3-sphere with minimal Heegaard Floer homology. We give the first examples of hyperbolic L-spaces with no symmetries. In particular, unlike all previously known L-spaces, these manifolds are not double branched covers of links in S^3. We prove the existence of infinitely many such examp…
Study of knot surgeries and JSJ decompositions to tackle L-space conjecture.
problem Understanding JSJ decompositions and L-space knots through Dehn surgeries. method Slope detection techniques applied to toroidal 3-manifolds and rational surgeries.
result JSJ graphs of certain knot exteriors are rooted intervals, implying left-orderable fundamental groups.
Paper tackles L-space conjecture for knot manifolds, proving equivalence for some properties.
problem Tackles L-space conjecture for knot manifolds, proving equivalence for some properties. method Introduces relative L-space conjecture, characterizes slope detection, uses Heegaard Floer homology, left-orders, and foliations. result Confirms equivalence of CTF and NLS for slope detected knots, identifies exceptional slopes. Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.
problem Prove properties of fundamental groups of toroidal 3-manifolds.
method Slope detection using left-orders, foliations, and Heegaard Floer homology.
result Toroidal integer homology spheres have left-orderable fundamental groups.
(1,1) non-L-space knots are foliar in 3D space.
problem Proving (1,1) non-L-space knots are foliar.
method Analyzing (1,1) non-L-space knots in S3 and lens spaces. result (1,1) non-L-space knots are persistently foliar.
The paper examines surgeries on 2-component L-space links and identifies key properties of the components.
problem Analyzing L-space surgeries on 2-component L-space links.
method Examining very negative surgeries and characterizing torus links.
result Identifies components of 2-component L-space links and characterizes specific links.
An L-space link is a link in S3 on which all large surgeries are L-spaces. In this paper, we initiate a general study of the definitions, properties, and examples of L-space links. In particular, we find many hyperbolic L-space links, including some chain links and two-bridge links; from them, we obtain many…
Classifies 3-braids as L-space knots.
problem Identifying L-space knots among 3-braids.
method Classification based on L-space properties.
result Closed 3-braids classified as L-space knots.
Characterizes knots with L-space surgeries in 3-sphere and lens spaces.
problem Identifying knots with specific L-space surgeries.
method Characterization of (1,1) knots and braids in 3-sphere and lens spaces.
result Characterizes knots with non-trivial L-space surgeries.
Paper constructs infinitely many non-braid positive hyperbolic L-space knots.
problem Proving the non-braid positivity of hyperbolic L-space knots.
method Constructs infinitely many hyperbolic L-space knots that are not braid positive.
result Distinct examples from Baker and Kegel's constructions.
L-spaces were introduced by Ozsvath and Szabo using the Heegaard Floer Homology. In the quest for L-spaces we consider links of isolated complete intersection surface singularities. We show that if such a manifold is an L-space, then it is a link of a rational singularity. We also prove that if it is not an L-space the…
New infinite family of knots found with unique properties.
problem Finding asymmetric L-space knots with specific properties.
method Generalizing known asymmetric L-space knot t12533 to form an infinite family.
result First infinite family of asymmetric hyperbolic L-space knots of braid index 4.
A knot in the 3-sphere is called an L--space knot if it admits a nontrivial Dehn surgery yielding an L--space. Like torus knots and Berge knots, many L--space knots admit also a Seifert fibered surgery. We give a concrete example of a hyperbolic, L-space knot which has no exceptional surgeries, in particular, no Seifer…
The paper explores fibered and quasi-positive links, introducing new families and invariants.
problem Understanding the structure of L-space links and their properties. method Using the H-function as a concordance link invariant.
result Introduced a subfamily of fibered strongly quasi-positive L-space links and an infinite family of non-quasi-positive L-space links. Research classifies L-space knots using Floer simple manifolds.
problem Understanding L-space fillings and their topological significance.
method Topological characterisation of Floer simple manifolds and classification of L-space knots.
result Partial classification of L-space twisted torus knots.
Study proves chainmail links are L-space links.
problem Understanding L-space links in chainmail links.
method Inspired by alternating links, uses flat augmentation.
result Proves alternating chainmail links are L-space links.
The study examines quasi-alternating surgeries on knots and their properties.
problem Understanding quasi-alternating surgeries and their relation to L-space knots.
method Exploration of quasi-alternating surgeries, classification of knots, and analysis of slopes.
result All SnapPy census L-space knots except two admit quasi-alternating surgeries.
L-space knots lack essential Conway spheres, proven with Floer theory.
problem Essential Conway spheres in L-space knots.
method Floer theoretic invariant for tangles.
result L-space knots have no essential Conway spheres.
New infinite family of hyperbolic L-space knots with specific semigroups.
problem Characterizing semigroups of L-space knots.
method Defined formal semigroups from Alexander polynomials and analyzed hyperbolic knots.
result Found an infinite family of hyperbolic L-space knots with semigroups generated by five elements.
An L-space link is a link in S3 on which all sufficiently large integral surgeries are L-spaces. We prove that for m, n relatively prime, the r-component cable link Krm,rn is an L-space link if and only if K is an L-space knot and n/m≥2g(K)−1. We also compute HFL-minus and HFL-hat of an L-space cable lin…
Formula for Upsilon invariant of L-space cable knots derived.
problem Calculating the Upsilon invariant for L-space cable knots.
method Using p,ΥK and ΥTp,q to derive a formula. result Integral values of the Upsilon invariant as a knot concordance invariant.
New patterns create satellite knots with special surgeries.
problem Creating knots with specific surgical properties.
method Sufficient conditions for satellite knots to have L-space surgeries.
result New infinite families of patterns for satellite L-space knots.
Knots formed from torus knots are not concordant to L-space knots.
problem Understanding concordance in knots formed from connected sums of torus knots.
method Analyzing properties of knots formed from connected sums of torus knots.
result Knots formed from torus knots are not concordant to L-space knots.
Classifies L-space surgeries on all two-bridge links
problem Classifying L-space surgeries on two-bridge links method Introduces a sufficient diagrammatic condition for links in S3 to be persistently foliar, defines a simplified model for Heegaard Floer homology, and uses Turaev torsions for computations result Determines L-space surgeries in the case of generalised L-space links Ozsvath-Szabo invariant classifies tight contact structures on L-spaces.
problem Classifying tight contact structures on L-spaces.
method Ozsvath-Szabo contact invariant.
result Complete classification invariant for tight contact structures.
Paper classifies CFK∞ type of almost L-space knots.
problem Understanding almost L-space knots and their properties.
method Utilizes Heegaard Floer homology and knot Floer homology.
result Classifies CFK∞ type of almost L-space knots. Researchers calculate link Floer homology for 2-component L-space links.
problem Computing link Floer homology for specific L-space links.
method Using the h-function of the filtered chain complex determined by Alexander polynomials. result Explicit determination of Thurston polytope and norm for 2-component L-space links.
New knots found that can't be turned into L-space after surgery.
problem Finding knots that can't be transformed into L-space after surgery.
method Examined algebraically concordant torus knots and fibred knots.
result Infinitely many knots of genus g≥2 cannot be turned into L-space. Study shows some knots can't be concordant to L-space knots.
problem Identifying knots that cannot be concordant to L-space knots.
method Used methods by Friedl, Livingston, and Zentner.
result Found knots that are not algebraically concordant to L-space knots.
Study concordance of alternating torus knots to L-space knots.
problem When are linear combinations of alternating torus knots concordant to L-space knots?
method Proved Allen's conjecture for alternating torus knots and established a necessary condition.
result Linear combinations of alternating torus knots are concordant to L-space knots if and only if they are a single torus knot.
New asymmetric L-space knots found in 3D space.
problem Finding asymmetric L-space knots in 3D space.
method Construction of hyperbolic knots with specific properties.
result First asymmetric L-space knots in S3 and lens spaces. New family of knots with L-space surgeries but not algebraic.
problem Characterizing knots with L-space surgeries.
method Infinite family construction and new semigroup invariant.
result No nontrivial linear combination of knots in the family is concordant to an algebraic knot.
Two knots with unique surgery properties.
problem Characterizing strongly invertible L-space knots.
method Examined surgeries and knot properties.
result Found knots whose surgeries are never Khovanov thin.
Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be cla…
Study shows surgeries on specific links result in L-spaces.
problem Understanding surgeries on specific links and their outcomes.
method Proving surgeries on chainmail links yield L-spaces using alternating surgeries.
result Alternating surgeries on chainmail links result in total L-spaces.
We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable. Examples of strong L-spaces include the double branched covers of alternating link…
It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below…
Study shows differences of torus knots do not form L-space knots.
problem Understanding concordance of knots and their relation to L-space knots. method Examined differences of torus knots and their concordance properties.
result Subgroups generated by two positive torus knots contain no nontrivial L-space knots. Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight …
Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of L-space knots, contained in the d-invariants of large surgeries. Generalizations…
We prove that a sufficiently large surgery on any algebraic link is an L-space. For torus links we give a complete classification of integer surgery coefficients providing L-spaces.
Study calculates instanton Floer homology for surgeries on L-space knots.
problem Computing the framed instanton Floer homology of surgeries on L-space knots.
method Used Baldwin-Sivek contact invariant and proved homogeneity of the invariant.
result Framed instanton Floer homology agrees with Heegaard Floer homology for L-space knots.
6 out of 29 dodecahedral 3-spheres are L-spaces, solving a Seiberg-Witten question.
problem Identifying L-spaces among dodecahedral 3-spheres.
method L-space census algorithm and hyperbolic geometry analysis.
result Existence of hyperbolic 4-manifolds with separating L-spaces.