Related papers: Null surgery on knots in L-spaces

A Seifert surface F for a knot K is free if the complement of F is a handlebody (i.e., has free fundamental group). The free genus of K is the minimum genus among all free Seifert surfaces for K. In this paper we show that there exist…

Using the mapping cone of a rational surgery, we give several obstructions for Seifert fibered surgeries, including obstructions on the Alexander polynomial, the knot Floer homology, the surgery coefficient and the Seifert and four-ball…

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…

A regular fiber of the Seifert fibering of the Poincar\'e homology sphere admits a Dehn surgery to $L(2,1)\#L(3,2)\#L(5,4)$. We prove that this is the only knot in the Poincar\'e homology sphere with a surgery to a connected sum of more…

Let W -> X be a real smooth projective 3-fold fibred by rational curves. J. Koll\'ar proved that, if W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces.…

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted.…

Distinct knots K, K' can sometimes share a common p/q-framed Dehn surgery. A folk conjecture held that for a fixed pair of knots, this can occur for at most one value of p/q. We disprove this conjecture by constructing pairs of distinct…

We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if $\frac 1{q_1-1} + \frac 1{q_2-1} + \frac 1{q_3-1} \leq 1$ then a Montesinos knot $K(\frac{p_1}{q_1}, \frac{p_2}{q_2}, \frac{p_3}{q_3})$…

Expanding on work by Conway, Orson, and Powell, we study the isotopy classes rel. boundary of nonorientable, compact, locally flatly embedded surfaces in $D^4$ with knot group $\mathbb{Z}_2$. In particular we show that if two such surfaces…

We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in $S^3$. In contrast with previously known examples, our proofs do not require any gauge theory or…

Fintushel and Stern have proved that if S \subset X is a symplectic surface in a symplectic 4-manifold such that S has simply-connected complement and nonnegative self-intersection, then there are infinitely many topologically equivalent…

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…

In this paper, we study reducible surgeries on knots in $S^3$. We develop thickness bounds for L-space knots that admit reducible surgeries, and lower bounds on the slice genus for general knots that admit reducible surgeries. The L-space…

The purpose of this paper is to study geometrically simply-connected homotopy 4-spheres by analyzing $n$-component links with a Dehn surgery realizing $\#^n(S^1\times S^2)$. We call such links $n$R-links. Our main result is that a homotopy…

Let K be a nontrivial knot in the 3-sphere with the exterior E(K), and u in G(K), the fundamental group of E(K), a slope element represented by an essential simple closed curve on the boundary of E(K). Since the normal closure of u in G(K)…

Suppose that a hyperbolic knot in $S^3$ admits a finite surgery, Boyer and Zhang proved that the surgery slope must be either integral or half-integral, and they conjectured that the latter case does not happen. Using the correction terms…

We show that on a hyperbolic knot $K$ in $S^3$, the distance between any two finite surgery slopes is at most two and consequently there are at most three nontrivial finite surgeries. Moreover in case that $K$ admits three nontrivial finite…

In this article, we demonstrate that for any positive integer $n$, the knot surgery $4$-manifold $E(n)_K$ has a handle decomposition without $1$- and $3$-handles. Here, $K$ represents either a fibered two-bridge knot $C(2\epsilon_1,…

We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we call the rational slice genus, that measures the complexity of a homology class in $H_2(Y\times [0,1],K;\mathbb{Q})$. Our main theorem is a…

Let N be a closed, oriented 3-manifold. A folklore conjecture states that $S^{1} \times N$ admits a symplectic structure if and only if $N$ admits a fibration over the circle. We will prove this conjecture in the case when N is irreducible…