arXiv research

(1,1) non-L-space knots are foliar in 3D space.

Paper constructs infinitely many non-braid positive hyperbolic L-space knots.

Characterizes knots with L-space surgeries in 3-sphere and lens spaces.

Study shows surgeries on specific links result in L-spaces.

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…

New description of $(1,1)$ L-space knots leads to non-left-orderable surgeries.

The paper finds infinite families of non-left-orderable L-spaces from tangles.

Paper finds infinitely many 3-spheres without nice orderings.

Study extends contact cosmetic surgeries to non-trivial Legendrian knots in L-spaces.

We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space.

Research classifies L-space knots using Floer simple manifolds.

Dehn filling on $v2503$ creates non-orderable spaces.

We show that a class of 3-manifolds with non left-orderable fundamental group are Heegaard Floer homology L-spaces

Constructs taut foliations for surgeries on positive 3-braids, confirming L-space conjecture.

In this paper we look at the knot complement problem for L-space $\mathbb{Z}$-homology spheres. We show that an L-space $\mathbb{Z}$-homology sphere $Y$ cannot be obtained as a non-trivial surgery along a knot $K\subset Y$. As a consequence, we prove that knots in an L-space $\mathbb{Z}$-homology sphere are determined …

Study shows non-left-orderable surgeries for specific L-space knots.

The study confirms conjectures about slopes of knots using knot Floer homology.

New findings on $L$-spaces and taut foliations in hyperbolic links.

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…

Classifies $L$-space surgeries on all two-bridge links

Let $P(K)$ be a satellite knot where the pattern, $P$, is a Berge-Gabai knot (i.e., a knot in the solid torus with a non-trivial solid torus Dehn surgery), and the companion, $K$, is a non-trivial knot in $S^3$. We prove that $P(K)$ is an L-space knot if and only if $K$ is an L-space knot and $P$ is sufficiently positi…

In hyperbolic L-spaces, we find multiple pseudo-Anosov flows with unique properties.

Study proves non-left-orderability of 3-manifolds derived from specific knots.

The paper examines surgeries on 2-component L-space links and identifies key properties of the components.

Study of knot surgeries and JSJ decompositions to tackle $L$-space conjecture.

New findings on branched covers of quasipositive links and their L-space properties.

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…

An $L$-space link is a link in $S^3$ 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…

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complet…

Classifies 3-braids as L-space knots.

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since large classes of L-spaces can be produced from Dehn surgery on knots in the 3-sphere, it is natural to ask what conditions on the knot group are suffi…

Let $K$ be a non-trivial knot in $S^3$, and let $r$ and $r'$ be two distinct rational numbers of same sign, allowing $r$ to be infinite; we prove that there is no orientation-preserving homeomorphism between the manifolds $S^3_r(K)$ and $S^3_{r'}(K)$. We further generalize this uniqueness result to knots in arbitrary i…

New findings on knots and their traces, distinguishing L-space knots by their 0-trace.

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 …

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 foliations found in 3D spaces from positive braids.

New infinite family of knots found with unique properties.

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.

Study proves chainmail links are L-space links.

This paper proves the Boyer-Gordon-Watson conjecture for 1-bridge braids.

We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…

The study examines quasi-alternating surgeries on knots and their properties.

L-space knots lack essential Conway spheres, proven with Floer theory.

New infinite family of hyperbolic L-space knots with specific semigroups.

An L-space link is a link in $S^3$ on which all sufficiently large integral surgeries are L-spaces. We prove that for m, n relatively prime, the r-component cable link $K_{rm,rn}$ is an L-space link if and only if K is an L-space knot and $n/m \geq 2g(K)-1$. We also compute HFL-minus and HFL-hat of an L-space cable lin…

Formula for Upsilon invariant of L-space cable knots derived.

New patterns create satellite knots with special surgeries.