Related papers: Fibered knots with the same $0$-surgery and the sl…

Closed 3-string braids admit many bandings to two-bridge links. By way of the Montesinos Trick, this allows us to construct infinite families of knots in the connected sum of lens spaces L(r,1) # L(s,1) that admit a surgery to a lens space…

In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for…

We show that, for each integer n, there exist infinitely many pairs of n-framed knots representing homeomorphic but non-diffeomorphic (Stein) 4-manifolds, which are the simplest possible exotic 4-manifolds regarding handlebody structures.…

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.

We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of…

The unknotting number $u$ and the genus $g$ of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus $g$ knot contains $g$ crossings, such that changing them produces…

Much work has been done on the existence and uniqueness of broken Lefschetz fibrations such as those by Auroux et al., Gay and Kirby, Lekili, Akbulut and Karakurt, Baykur, and Williams, but there has been a lack of explicit examples. A…

The Cabling Conjecture of Gonz\'alez-Acu\~na and Short holds that only cable knots admit Dehn surgery to a manifold containing an essential sphere. We approach this conjecture for thin knots using Heegaard Floer homology, primarily via…

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…

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.…

While equality of skew Schur functions is well understood, the problem of determining when two skew Schur $Q$ functions are equal is still largely open. It has been studied in the case of ribbon shapes in 2008 by Barekat and van…

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…

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 $K\subset Y$…

We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants $\widetilde{\operatorname{Kh}}$ and…

Band surgery is an operation relating pairs of knots or links in the three-sphere. We prove that if two quasi-alternating knots $K$ and $K'$ of the same square-free determinant are related by a band surgery, then the absolute value of the…

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…

Given any knot K in the 3-sphere, we prove that there are only finitely many hyperbolic fibered knots which are ribbon concordant to K. It follows that every fibered knot in the 3-sphere has only finitely many hyperbolic predecessors under…

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 recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are…

We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.