Related papers: A construction of slice knots via annulus twists
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).
We define an operation on homology ${B}^4$ which we call an $n$-twist annulus modification. We give a new construction of smoothly slice knots and exotically slice knots via $n$-twist annulus modifications. As an application, we present a…
A pretzel knot $K$ is called $odd$ if all its twist parameters are odd, and $mutant$ $ribbon$ if it is mutant to a simple ribbon knot. We prove that the family of odd, 5-stranded pretzel knots satisfies a weaker version of the Slice-Ribbon…
Take a thin, rectangular strip of paper, add in an odd number of half-twists, then join the ends together. This gives a multi-twist paper M\"obius band. We prove that any multi-twist paper M\"obius band can be constructed so the aspect…
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.
The $T$-genus of a knot is the minimal number of borromean-type triple points on a normal singular disk with no clasp bounded by the knot; it is an upper bound for the slice genus. Kawauchi, Shibuya and Suzuki characterized the slice knots…
We determine the smooth concordance order of the 3-stranded pretzel knots P(p,q,r) with p,q,r odd. We show that each one of finite order is, in fact, ribbon, thereby proving the slice-ribbon conjecture for this family of knots. As…
We establish the slice-ribbon conjecture for a large family of Montesinos' knots by means of Donaldson's theorem on the intersection forms of definite 4-manifolds.
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…
The twisting number of a ribbon knot $K$ is the minimal number of tangle replacements on the symmetry axis of $J \# -J$ for any knot $J$ that is required to produce a symmetric union diagram of $K$. We prove that the twisting number is…
A closer look at an example introduced by Livingston & Melvin and later studied by Miyazaki shows that a plumbing of two fibered ribbon knots (along their fiber surfaces) may be algebraically slice yet not ribbon.
We define an obstruction for a knot to be Z[Z]-homology ribbon, and use this to provide restrictions on the integers that can occur as the triple linking numbers of derivative links of knots that are either homotopy ribbon or doubly slice.…
We give a complete characterization of the topological slice status of odd 3-strand pretzel knots, proving that an odd 3-strand pretzel knot is topologically slice if and only if either it is ribbon or has trivial Alexander polynomial. (By…
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of…
Here, we prove that $0-$shake slice knots are slice.
In this paper we show how to realize all knot (and link) types as C^{2} smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "building blocks" that are particular…
This paper presents a construction of a folded paper ribbon knot that provides a constant upper bound on the infimal aspect ratio for paper M\"obius bands and annuli with arbitrarily many half-twists. In particular, the construction shows…
The concordance group of algebraically slice knots is the subgroup of the classical knot concordance group formed by algebraically slice knots. Results of Casson and Gordon and of Jiang showed that this group contains in infinitely…
In this note we show that ribbon concordance forms a partial ordering on the set of knots, answering a question of Gordon. The proof makes use of representation varieties of the knot groups to $SO(N)$ and relations between them induced by a…