Related papers: $0$-Shake Slice Implies Slice

A proof that $0-$shake slice knots are slice.

Here we discuss $r-$shake slice knots, and their relation to corks, we then prove that $0$-shake slice knots are slice.

Shake slice generalizes the notion of a slice link, naturally extending the notion of shake slice knots to links. There is also a relative version, shake concordance, that generalizes link concordance. We show that if two links are shake…

A crucial step in the surgery-theoretic program to classify smooth manifolds is that of representing a middle--dimensional homology class by a smoothly embedded sphere. This step fails even for the simple 4-manifolds obtained from the…

We construct infinitely many smoothly slice knots having topological slice discs that are non-approximable by smooth slice discs.

A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all…

Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of S^n. We show that all frame-spun knots are slice (null-cobordant).

A knot in $S^3$ is topologically slice if it bounds a locally flat disk in $B^4$. A knot in $S^3$ is rationally slice if it bounds a smooth disk in a rational homology ball. We prove that the smooth concordance group of topologically and…

A knot K in the 3-sphere is superslice if there is a slice disk D in the 4-ball such that the double of D along K is the unknotted 2-sphere S in $S^4$. Answering a question of Livingston-Meier, we find smoothly slice (in fact doubly slice)…

The main goal of this paper is to prove that for odd free knots - that is free knots with all odd crossings - the problem of sliceness (the existence of a spanning disc) has an explicit answer based on the pairing of the knot diagram…

For n >1, if the Seifert form of a knotted 2n-1 sphere K in S^{2n+1} has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three (n = 1). However, in the three dimensional case it is true that…

We define a notion of complexity for shake-slice knots which is analogous to the definition of complexity for h-cobordisms studied by Morgan-Szab\'o. We prove that for each framing $n \ne 0$ and complexity $c \ge 0$, there is an…

We prove that there exist infinitely many topologically slice knots which cannot bound a smooth null-homologous disk in any definite 4-manifold. Furthermore, we show that we can take such knots so that they are linearly independent in the…

A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, is not slice. This completes the classification of slice knots under 13 crossings, and…

We investigate the properties of knots in S^3 which bound Klein bottles, such that a pushoff of the knot has zero linking number with the knot, i.e. has zero framing. This is motivated by the many results in the literature regarding slice…

A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50 years, it was unknown whether a certain 11 crossing knot, called the Conway knot, was slice or not, and until recently, this was the only one of the thousands of…

We give a new construction of slice knots via annulus twists. The simplest slice knots obtained by our method are those constructed by Omae. In this paper, we introduce a sufficient condition for given slice knots to be ribbon, and prove…

We establish a number of results about smooth and topological concordance of knots in $S^1\times S^2$. The winding number of a knot in $S^1\times S^2$ is defined to be its class in $H_1(S^1\times S^2;\mathbb{Z})\cong \mathbb{Z}$. We show…

It is known that the linking form on the 2-cover of slice knots has a metabolizer. We show that several weaker conditions, or some other conditions related to sliceness, do not imply the existence of a metabolizer. We then show how the…

We prove the existence of a smoothly doubly slice, amphicheiral knot with Alexander polynomial 1 and unknotting number 5.