arXiv research

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

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

New hyperbolic knots not concordant to algebraic ones found.

New infinite family of knots found with unique properties.

Paper finds first infinite family of hyperbolic knots with specific 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…

6 out of 29 dodecahedral 3-spheres are L-spaces, solving a Seiberg-Witten question.

A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c and twist K n times along c to obtain a twist family { K_n }. We give a sufficient…

Classifies tight contact structures on surgeries of the Whitehead link.

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…

New knots share same Upsilon invariant despite different Alexander polynomials.

We find braid positive presentations for most L-space knots, except one, and explore related knot properties.

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…

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…

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

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

The study finds knots with specific surgeries that don't allow weak symplectic fillings.

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

Study Froyshov invariants and closed geodesics in hyperbolic 3-manifolds.

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

Researchers prove Seifert-Weber dodecahedral space is an L-space.

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 …

Study shows hyperbolic knots' monodromy without fixed points.

In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$ manifolds contain $9$ asymmetric L-space knot complements. Furthermore, using SnapPy a…

We construct taut foliations in every closed 3-manifold obtained by $r$-framed Dehn surgery along a positive 3-braid knot $K$ in $S^3$, where $r < 2g(K)-1$ and $g(K)$ denotes the Seifert genus of $K$. This confirms a prediction of the L-space Conjecture. For instance, we produce taut foliations in every non-L-space obt…

We show the existence of hyperbolic 4-manifolds with vanishing Seiberg-Witten invariants, addressing a conjecture of Claude LeBrun. This is achieved by showing, using results in geometric and arithmetic group theory, that certain hyperbolic 4-manifolds contain L-spaces as hypersurfaces.

Let $D$ be a diagram of an alternating knot with unknotting number one. The branched double cover of $S^3$ branched over $D$ is an L-space obtained by half integral surgery on a knot $K_D$. We denote the set of all such knots $K_D$ by $\mathcal D$. We characterize when $K_D\in \mathcal D$ is a torus knot, a satellite k…

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

The paper constructs 3-manifolds with co-orientable taut foliations but no foliations with vanishing Euler class.

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

The study connects twist positivity to L-space knots and concordance.

Study on reducing surgeries on knots, developing thickness and genus bounds.

Formula for Casson-Walker invariant; applies to knot complements and cosmetic crossing conjecture.

There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; in the case that the first Betti number is zero this property is closely tied to the existence of certain nice foliation…

The study finds many tight contact structures on hyperbolic 3-spheres.

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

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…

A slope $p/q$ is a characterising slope for a knot $K$ in $S^3$ if the oriented homeomorphism type of $p/q$-surgery on $K$ determines $K$ uniquely. We show that when $K$ is a hyperbolic knot its set of characterising slopes contains all but finitely many slopes $p/q$ with $q \geq 3$. We prove stronger results for hyper…

The paper extends techniques to create non-left-orderable manifolds from links with multiple boundary components.

New invariants from framed instanton homology for knot concordance.

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…

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

Study proves chainmail links are L-space links.

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

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

Classifies knots in the Poincaré sphere, using fixed points and folding automata.

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…