Related papers: Slicing Bing doubles
We show that any strongly negative amphichiral knot with a trivial Alexander polynomial is equivariantly topologically slice.
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
A knitted surface is a surface with or without closed components smoothly properly embedded in $D^2 \times B^2$, which is a generalization of a braided surface. A knitted surface is called a 2-dimensional knit if its boundary is the closure…
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 define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose…
We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a…
The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman's work on topological surgery and Donaldson's gauge theoretic approach to 4-manifolds. Here, as an application of…
We show that perturbing the definition of sl(n) Khovanov-Rozansky link homology gives a lower bound on the slice genus of a knot. As a corollary this yields another proof of Milnor's conjecture on the slice genus of torus knots.
We show that if the branched double cover of an alternating link arises as $p/q \in \mathbb{Q} \setminus \mathbb{Z}$ surgery on a knot in $S^3$, then this is exhibited by a rational tangle replacement in an alternating diagram.
To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is…
We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for 4-dimensional surgery, is shown to admit Seifert surfaces with trivial Lagrangian. They are…
We prove that two polygons $A$ and $B$ have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between $A$ and $B$) if and only if $A$ and $B$ are two noncrossing nets of a…
We define the symmetric braid index $b_s(K)$ of a ribbon knot $K$ to be the smallest index of a braid whose closure yields a symmetric union diagram of $K$, and derive a Khovanov-homological characterisation of knots with $b_s(K)$ at most…
From the work of X. S. Lin and Z. Wang, it follows that degree two knot invariant admits a decomposition into the sum of a Gauss diagram count and a term involving Arnold invariants. In this paper we establish an analogous description for…
A surface-link is a closed surface embedded in the 4-space, possibly disconnected or non-orientable. Every surface-link can be presented by the plat closure of a braided surface, which we call a plat form presentation. The knot symmetric…
New presentations of a link and a virtual link are introduced and algebraic systems on links and virtual links are constructed respectively. Based on the algebraic systems, Reduction Crossing Algorithms for them are proposed which are used…
We start with a disk with $2n$ vertices along its boundary where pairs of vertices are connected with $n$ strips with certain restrictions. This forms a {\it pairing}. To relate two pairings, we define an operator called a cut-and-glue…
The simultaneous crossing number is a new knot invariant which is defined for strongly invertible knots having diagrams with two orthogonal transvergent axes of strong inversions. Because the composition of the two inversions gives a cyclic…
A binary tanglegram is a pair <S,T> of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics or software engineering, it is required…
An oriented link L in a 3-sphere S in complex 2-space is a C-boundary if it bounds a piece of algebraic curve in the 4-ball bounded by S. Using Kronheimer and Mrowka's proof of the Thom Conjecture, we construct many oriented knots which are…