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.
New proof shows L-space knots are fibered and have specific properties.
problem Proving L-space knots are fibered and have strong quasipositive properties.
method Conceptually simpler proof using Heegaard Floer homology, translated to instanton Floer homology.
result Generalization of L-space knot properties to other Floer homologies.
New insights into knot surgeries via instanton 2-torsion.
problem Understanding rational surgeries on knots and their implications.
method Extending earlier results on integral surgeries to rational surgeries using framed instanton homology.
result If framed instanton homology is 2-torsion-free, the knot is an instanton L-space knot and the surgery parameter is greater than 2g(K)-1.
Enhances knot surgery formulae for instanton Floer homology.
problem Calculating instanton Floer homology for various 3-manifolds.
method Integral surgery formulae and rational surgery formulae for null-homologous knots.
result Characterizes instanton Floer homology of specific 3-manifolds and knots.
Study knots with bounded SU(2)-cyclic slopes and unique limit point.
problem Infinitely many SU(2)-cyclic surgeries on knots. method Holonomy perturbation techniques applied to instanton knot homology.
result Knots have bounded SU(2)-cyclic slopes with a unique limit point. Proves exact triangle linking knot instanton Floer homology to surgeries.
problem Relating knot instanton Floer homology to surgeries.
method Proves an exact triangle using integer coefficients.
result Poincaré Homology Sphere is not an instanton L-space with integer coefficients.
Instantons prove knots are fibered and strongly quasipositive.
problem Proving properties of knots using instantons and L-space surgeries.
method New cobordism maps in framed instanton Floer homology.
result Proves fibered and strongly quasipositive knots have specific homomorphisms.
The paper examines 2-torsion in instanton Floer homology for knots and 3-manifolds.
problem Existence of 2-torsion in instanton Floer homology for knots and 3-manifolds.
method Analyzes framed and singular instanton Floer homology, uses lemmas from Heegaard Floer theory.
result Shows existence of 2-torsion in instanton Floer homology for various knots and 3-manifolds.
New invariants from framed instanton homology for knot concordance.
problem Concordance of knots and their properties.
method Framed instanton homology to define invariants.
result Computations and bounds on knot concordance invariants.
New proof shows certain 3D shapes can't be instanton L-spaces.
problem Proving certain 3D shapes cannot be instanton L-spaces.
method Proving by gluing complements of knots and analyzing their fundamental groups.
result Proven that the resulting 3-manifold cannot be an instanton L-space.
Sutured instanton homology uses Heegaard diagrams to bound homology dimensions.
problem Bounding the dimension of sutured instanton homology.
method Using admissible Heegaard diagrams, proving a bound on the number of generators of the associated sutured Heegaard Floer complex.
result Strong L-spaces are instanton L-spaces.
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…
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…
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.
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…
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.
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.
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 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.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
Study extends contact cosmetic surgeries to non-trivial Legendrian knots in L-spaces.
problem Contact cosmetic surgeries for Legendrian knots in L-spaces.
method Adapting techniques from S3 to L-spaces, incorporating Heegaard Floer theory constraints.
result Contact cosmetic surgery conjecture holds for non-trivial Legendrian knots, except for Lagrangian slice knots.
We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge about which knots in S^3 admit lens space surgeries.
New infinite family of knots without special surgeries found.
problem Finding knots without specific surgeries.
method Identifying an infinite family of knots.
result First infinite family of strongly invertible L-space knots without Khovanov thin surgery.
Constructs taut foliations for surgeries on positive 3-braids, confirming L-space conjecture.
problem Confirming the L-space conjecture for surgeries on positive 3-braids.
method Constructs taut foliations in 3-manifolds obtained by r-framed Dehn surgery along positive 3-braids. result Confirms the L-space conjecture for surgeries on positive 3-braids.
Researchers compute link surgery modules for 2-component L-space links.
problem Computing the link surgery modules of 2-component L-space links.
method Koszul duality to extend earlier computations.
result Computed entire link surgery modules modulo a technical result.
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. 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…
New description of (1,1) L-space knots leads to non-left-orderable surgeries.
problem Characterizing and understanding (1,1) L-space knots. method Analyzing coherent reduced (1,1)-diagrams to describe (1,1) L-space knots and proving non-left-orderable fundamental groups. result Any L-space obtained by Dehn surgery on a (1,1)-knot in S3 has a non-left-orderable fundamental group. 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.
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.
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.
The study finds knots with specific surgeries that don't allow weak symplectic fillings.
problem Detecting weakly symplectic fillability of L-space knots after positive surgeries. method Analyzing arithmetic data from knot type and surgery coefficients to compute geometric invariants.
result Provides an infinite family of hyperbolic L-spaces that do not admit weakly symplectic fillings. We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of L-space knots, every sufficiently large surgery may be realized as the two-fold branch…
We prove that the (p,q)-cable of a knot K in S^3 admits a positive L-space surgery if and only if K admits a positive L-space surgery and q/p \geq 2g(K)-1, where g(K) is the Seifert genus of K. The "if" direction is due to Hedden.
Study shows non-left-orderable surgeries for specific L-space knots.
problem Understanding left-orderability of surgeries on L-space knots.
method Analyzing L-space twisted torus knots and their surgeries.
result Fundamental groups of certain surgeries are not left-orderable.
Computes upper bounds for instanton knot homology.
problem Computing the exact dimension of instanton knot homology.
method Developed an algorithm using knot diagrams and Heegaard diagrams.
result Algorithm provides sharp bounds for knots up to seven crossings.
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.
Whitehead link surgeries are not L-spaces if they support taut foliations.
problem Characterizing rational homology spheres as L-spaces.
method Analyzing Whitehead link surgeries and their foliations.
result Whitehead link surgeries are not L-spaces if they support coorientable taut foliations.
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. New insights into L-space surgeries on multi-component links and satellites.
problem Characterizing rational surgery slopes yielding L-spaces for multi-component links.
method Generalizing Hedden and Hom's results for cables, computing L for satellites by torus-links and algebraic links. result Explicit descriptions of L for rational surgeries on multi-component links and satellites. A rational homology sphere whose Heegaard Floer homology is the same as that of a lens space is called an L-space. We classify pretzel knots with any number of tangles which admit L-space surgeries. This rests on Gabai's classification of fibered pretzel links.
Knots in L-spaces with certain surgeries are rationally fibered and have tight contact structures.
problem Characterizing knots in L-spaces and their surgeries.
method Analyzing Dehn surgeries, Thurston norm minimization, and Floer homology.
result Knots in L-spaces with specific surgeries are rationally fibered and induce tight contact structures.
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…
In this paper, we use Heegaard Floer homology to study reducible surgeries. In particular, suppose K is a non-cable knot in the three-sphere with an L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1. This implies that any knot with an L-space surgery has at most one reducible surgery, a fac…
New findings on L-spaces and taut foliations in hyperbolic links.
problem Characterizing L-spaces and taut foliations in Dehn surgeries on hyperbolic links. method Analyzing rational homology spheres and using coorientable taut foliations.
result Non-meridional surgeries on fibered hyperbolic two-bridge links support coorientable taut foliations.
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…