arXiv research

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

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

Proves rational slopes characterize knot 5_2, except for integers.

Enhances knot surgery formulae for instanton Floer homology.

Hedden defined two knots in each lens space that, through analogies with their knot Floer homology and doubly pointed Heegaard diagrams of genus one, may be viewed as generalizations of the two trefoils in S^3. Rasmussen shows that when the `left-handed' one is in the homology class of the dual to a Berge knot of type …

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

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

New infinite family of knots found with unique properties.

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

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…

Study concordance of alternating torus knots to L-space knots.

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

New hyperbolic knots not concordant to algebraic ones found.

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

Two knots with unique surgery properties.

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

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 …

Characterizes $(1,1)$ knots with large Dehn surgeries.

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

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…

New knots share same Upsilon invariant despite different Alexander polynomials.

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

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

We give sufficient conditions for a satellite knot to admit an L-space surgery, and use this result to give new infinite families of patterns which produce satellite L-space knots.

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

The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.

Algebraic knots are known to be iterated torus knots and to admit L-space surgeries. However, Hedden proved that there are iterated torus knots that admit L-space surgeries but are not algebraic. We present an infinite family of such examples, with the additional property that no nontrivial linear combination of knots …

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…

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 …

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

It is known that connected sums of positive torus knots are not concordant to $L$-space knots. Here we consider differences of torus knots. The main result states that the subgroup of the concordance group generated by two positive torus knots contains no nontrivial $L$-space knots other than the torus knots themselves…

We consider the following question: when is the manifold obtained by gluing together two knot complements an $L$-space? Hedden and Levine proved that splicing 0-framed complements of nontrivial knots never produces an $L$-space. We extend this result to allow for arbitrary integer framings. We find that splicing two in…

Study calculates instanton Floer homology for surgeries on L-space knots.

Formula for τ-invariant of satellite knots derived from L-space satellite operators.

We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery to an L-space, despite resembling algebraic knots and L-space knots in general: they are algebraically concordant to the torus knot $T(2,2g+1)$ of the same genus and they are fibred and strongly quasipositive.

If a knot is a nontrivial connected sum of positive torus knots, then it is not concordant to an L-space knot.

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…

We give a formula of the Upsilon invariant of any L-space cable knot $K_{p,q}$ using $p,Υ_K$ and $Υ_{T_{p,q}}$. The integral value of the Upsilon invariant gives a ${\mathbb Q}$-valued knot concordance invariant. We compute the integral values for L-space iterated cable knots.

Paper finds first infinite family of hyperbolic knots with specific properties.

We classify closed 3-braids which are L-space knots.

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

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

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

In this short note we use methods of Friedl, Livingston and Zentner to show that there are knots that are not algebraically concordant to a connected sum of positive and negative L-space knots.

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

Cables of L-space knots have multiplicative knot Floer order.

New proof shows most thin knots satisfy Cabling Conjecture.