Related papers: Cosmetic surgeries on genus one knots

Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets…

We give a necessary and sufficient condition for a simple closed curve on the boundary of a genus two handlebody to decompose the handlebody into (torus with one boundary component times [0,1]. We use this condition to decide whether a…

We give a diagrammatic characterization of the $(1,1)$ knots in the three-sphere and lens spaces which admit large Dehn surgeries to manifolds with Heegaard Floer homology of next-to-minimal rank. This is inspired by a corresponding result…

Supose that $Y$ is a lens space with $|H_1(Y; \mathbb{Z})|$ prime, and $Y$ does not contain a genus one fibered knot. We show that $Y$ contains a knot whose exterior is a once-punctured torus bundle if and only if $Y$ is the result of…

We show how one may sometimes perform singular ambient surgery on the complex locus of a real algebraic curve and obtain what we call a floppy curve. A floppy curve is a certain kind of singular surface in CP(2), more general than the…

Freedman and Krushkal showed that if the surgery conjecture and the $s$-cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking numbers is topologically round handle slice. Kim, Powell, and…

In this note, we prove that a nontrivial Kinoshita-Terasaka or Conway knot does not admit chirally cosmetic surgeries, by calculating the finite type invariant of order 3.

We consider homologically essential simple closed curves on Seifert surfaces of genus one knots in $S^3$, and in particular those that are unknotted or slice in $S^3$. We completely characterize all such curves for most twist knots: they…

We construct an infinite family of smoothly slice knots that we prove are topologically doubly slice. Using the correction terms coming from Heegaard Floer homology, we show that none of these knots is smoothly doubly slice. We use these…

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a non-trivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer…

We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem…

Let $Y_1$ be a closed, oriented 3-manifold and $\Sigma$ denote a non-separating closed, orientable surface in $Y_1$ which consists of two connected components of the same genus. By cutting $Y_1$ along $\Sigma$ and re-gluing it using an…

A pair of Dehn surgeries on a knot is called chirally cosmetic if they yield orientation-reversingly homeomorphic 3-manifolds. In this paper, we consider exceptional or half-integral chirally cosmetic surgeries, and obtain several…

Let $K$ be a knot in an L-space $Y$ with a Dehn surgery to a surface bundle over $S^1$. We prove that $K$ is rationally fibered, that is, the knot complement admits a fibration over $S^1$. As part of the proof, we show that if $K\subset Y$…

This paper studies the existence of $2$-torsion in instanton Floer homology with $\mathbb{Z}$ coefficients for closed $3$-manifolds and singular knots. First, we show that the non-existence of $2$-torsion in the framed instanton Floer…

In this paper, we set up two surgery theories and two kinds of Whitehead torsion for foliations. First, we construct a bounded surgery theory and bounded Whitehead torsion for foliations, which correspond to the Connes' foliation algebra in…

We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0-- or 1--crossing knot. The proof uses techniques from sutured manifold theory.

We prove that, for each fixed rational number $p/q \in \mathbb{Q}$, there exists a pair of distinct knots whose $p/q$-surgeries are orientation-preservingly homeomorphic. This confirms a 1978 conjecture of Gordon.

We use the LMO invariant to find constraints for a knot to admit a purely or reflectively cosmetic surgery. We also get a constraint for knots to admit a Lens space surgery, and some information for characterizing slopes.

We describe a procedure for creating infinite families of hyperbolic knots having unique minimal genus Seifert surface. A large subset of these knots have the further property that the surface cannot be the sole compact leaf of a depth one…