arXiv research

In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits very negative (i.e. $d_{1}, d_{2}\ll0$) L-space surgeries, it is the Hopf link. We also give a w…

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…

Study proves chainmail links are L-space links.

The paper explores fibered and quasi-positive links, introducing new families and invariants.

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…

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

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 shows surgeries on specific links result in L-spaces.

We compute different versions of link Floer homology $HFL^{-}$ and $\widehat{HFL}$ for any $L$-space link with two components. The main approach is to compute the $h$-function of the filtered chain complex which is determined by the Alexander polynomials of every sublink of the $L$-space link. As an application, Thurst…

Researchers compute link surgery modules for 2-component L-space links.

We will prove that, for a $2$ or $3$ component $L$-space link, $HFL^-$ is completely determined by the multi-variable Alexander polynomial of all the sub-links of $L$, as well as the pairwise linking numbers of all the components of $L$. We will also give some restrictions on the multi-variable Alexander polynomial of …

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…

We define and prove properties of link lattice complexes for plumbed links.

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…

Whitehead link surgeries are not L-spaces if they support taut foliations.

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…

Study Khovanov homology of positive links and L-space knots, finding vanishing conditions.

Formula for satellite operators using knot Floer homology.

We focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. In previous paper \cite{Usui}, we collect such manifolds systematically by using the smoothing order on links. In this paper, we classify such L-spaces under appropreate constraint.

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

Classifies tight contact structures on surgeries of the Whitehead link.

Study links with annuli using sutured Floer homology.

Paper classifies $CFK^\infty$ type of almost L-space knots.

Study on pretzel knots showing cyclic branched covers are L-spaces.

In this paper, we focus on L-spaces for which the boundary maps of the Heegaard Floer chain complexes vanish. We collect such manifolds systematically by using the smoothing order on links.

We construct the first examples of asymmetric L-space knots in $S^3$. More specifically, we exhibit a construction of hyperbolic knots in $S^3$ with both (i) a surgery that may be realized as a surgery on a strongly invertible link such that the result of the surgery is the double branched cover of an alternating link …

Let $L$ be a oriented link such that $Σ_n(L)$, the $n$-fold cyclic cover of $S^3$ branched over $L$, is an L-space for some $n \geq 2$. We show that if either $L$ is a strongly quasipositive link other than one with Alexander polynomial a multiple of $(t-1)^{2g(L) + (|L|-1)}$, or $L$ is a quasipositive link other than …

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

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…

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.

Given an $n$-component link $L$ in any 3-manifold $M$, the space $\mathcal{L} \subset (\mathbb{Q}\cup \mkern-1.5mu\{\infty\})^n$ of rational surgery slopes yielding L-spaces is already fully characterized (in joint work by the author) when $n\!=\!1$ and $\mathcal{L}$ is nontrivial. For $n\mkern-2mu>\mkern-3mu1$, howeve…

Two knots with unique surgery properties.

We investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched cover. In particular, we show that if $δ_n = σ_1 σ_2 \ldots σ_{n-1}$ is the dual …

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in $B^{4}$. In this paper, we describe the set of genera of such surfaces in terms of the $h$-function, which is a link invariant from Heegaard Floer homology. In particular, we use the $h$-function to give lower bou…

We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…

We prove that the link of a complex normal surface singularity is an L--space if and only if the singularity is rational. This via a recent result of Hanselman, J. Rasmussen, S. D. Rasmussen and Watson (proving the conjecture of Boyer, Gordon and Watson), shows that a singularity link is not rational if and only if its…

Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.

Study $d$-invariants of L-space double branched covers of arborescent links.

An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying $d$-invariant inequalities for this cobordism we obtain inequalities between the $H$-functions of links, whi…

Proves special alternating knots can't have cosmetic crossings.

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…

The paper characterizes L-space 3-manifolds using quandle orderability.

The paper explores nonexistence and existence of symplectic and Stein fillable contact structures on 3-manifolds.

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

The article proves properties of Seifert links and their cyclic branched covers.

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 shows inequality in Floer homologies for 3-manifold covers.

Conjecturally, there are only finitely many Heegaard Floer L-space knots in $S^3$ of a given genus. We examine this conjecture for twist families of knots $\{K_n\}$ obtained by twisting a knot $K$ in $S^3$ along an unknot $c$ in terms of the linking number $ω$ between $K$ and $c$. We establish the conjecture in case of…