Related papers: L-space surgeries on 2-component L-space links

We show that if $K$ is an L-space twisted torus knot $T^{l,m}_{p,pk \pm 1}$ with $p \ge 2$, $k \ge 1$, $m \ge 1$ and $1 \le l \le p-1$, then the fundamental group of the $3$-manifold obtained by $\frac{r}{s}$-surgery along $K$ is not…

We study lens space surgeries along two different families of 2-component links, denoted by $A_{m,n}$ and $B_{p,q}$, related with the rational homology 4-ball used in J.\ Park's (generalized) rational blow down. We determine which…

We study taut foliations on the complements of non-split positive braid closures in $S^3$. If $L$ is such a link with components $L_1,\ldots,L_n$ and at least one component is not the unknot, then the Dehn surgery along a multislope…

We present two examples of strongly invertible L-space knots whose surgeries are never the double branched cover of a Khovanov thin link in the 3-sphere. Consequently, these knots provide counterexamples to a conjectural characterization of…

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…

We consider satellite operators where the corresponding 2-component link is an L-space link. This family includes many commonly studied satellite operators, including cabling operators, the Whitehead operator, and a family of Mazur…

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…

In this article, we explore phenomena relating to quasi-alternating surgeries on knots, where a quasi-alternating surgery on a knot is a Dehn surgery yielding the double branched cover of a quasi-alternating link. Since the double branched…

We prove that if the lens space $L(n, 1)$ is obtained by a surgery along a knot in the lens space $L(3,1)$ that is distance one from the meridional slope, then $n$ is in $\{-6, \pm 1, \pm 2, 3, 4, 7\}$. This result yields a classification…

There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which knots are determined by which of their traces? We prove…

In this paper, we show that the lens space $L(s,1)$ for $s \neq 0 $ is obtained by a distance one surgery along a knot in the lens space $L(n,1)$ with $n \geq 5$ odd only if $n$ and $s$ satisfy one of the following cases: (1) $n \geq 5$ is…

The surgery unknotting number of a Legendrian link is defined as the minimal number of particular oriented surgeries that are required to convert the link into a Legendrian unknot. Lower bounds for the surgery unknotting number are given in…

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via…

This paper concerns the H(2)-unknotting numbers of links related to 2-bridge links. It consists of three parts. In the first part, we consider a necessary and sufficient condition for a 2-bridge link to have H(2)-unknotting number one. The…

We consider a relation between two kinds of unknotting numbers defined by using a band surgery on unoriented knots; the band-unknotting number and H(2)-unknotting number, which we may characterize in terms of the first Betti number of…

In this article, we apply slope detection techniques to study properties of toroidal $3$-manifolds obtained by performing Dehn surgeries on satellite knots in the context of the $L$-space conjecture. We show that if $K$ is an $L$-space knot…

A two-component link produces a torus as the product of the component knots in a two-point configuration space of a three-sphere. This space can be identified with a cotangent bundle and also with an indefinite Grassmannian. We show that…

For any knot T transverse to a given contact structure on a 3-manifold, we exhibit a Legendrian two-component link such that T equals the transverse push-off of one of the link components and contact (+1)-surgery on the link has the same…

It is well-known that the second coefficient of the Alexander polynomial of any lens space knot in $S^3$ is $-1$. We show that the non-zero third coefficient condition of the Alexander polynomial of a lens space knot $K$ in $S^3$ confines…

Let \Theta (M,K) denote the 2-loop piece of (the logarithm of) the LMO invariant of a knot K in M, a ZHS^3. Forgetting the knot (by which we mean setting diagrams with legs to zero) specialises \Theta (M,K) to \lambda (M), Casson's…