Related papers: Concordance properties of parallel links
Physical knots and links are one-dimensional submanifolds of R^3 with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical knot and link theory. In particular we exhibit a Gordian…
An edge cut C of a graph G is tight if |C \M| = 1 for every perfect matching M of G. Barrier-cuts and 2-separation cuts, also referred to as ELP-cuts, are two important types of tight cuts in matching covered graphs. Edmonds, Lovasz and…
Steinhaus conjectured that every closed oriented $C^1$-curve has a pair of anti-parallel tangents. Porter disproved the conjecture by showing that there exist curves with no anti-parallel tangents. Colin Adams rised the question of whether…
We study the equivariant 4-genus of strongly invertible knots in the $S^3$ boundary of 4-manifolds with involution. We provide techniques for constructing slice disks for knots in various symmetric 4-manifolds via an equivariant version of…
We study the equivariant concordance classes of two-bridge knots, providing an easy formula to compute their butterfly polynomial, and we give two different proofs that no two-bridge knot is equivariantly slice. Finally, we introduce a new…
We introduce a generalization of the Ozsv\'ath-Szab\'o $\tau$-invariant to links by studying a filtered version of link grid homology. We prove that this invariant remains unchanged under strong concordance and we show that it produces a…
In 2000, Habiro introduced the notion of $C_k$-equivalence of knots and links. This geometric filtration is closely connected to finite type invariants, a class of invariants including Milnor's invariants. Shortly thereafter, Ohyama,…
We show that a $(p,q)$-cable of a non-trivial knot $K$ does not admit chirally cosmetic surgery for $q\neq 2$, or $q=2$ with additional assumptions. In particular, we show that $(p,q)$-cable of non-trivial knot $K$ does not admit chirally…
For all n > 0 there is a homomorphism from the smooth concordance group of knots in dimension 2n + 1 to an algebraically defined group called the rational algebraic concordance group. This algebraic concordance group splits as a direct sum…
This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components.…
We describe a symmetry breaking construction in coarse geometry which allows to obtain information about equivariant coarse homology classes by restriction to smaller groups and spaces. In the case of equivariant coarse $K$-homology theory…
We establish several results about two short exact sequences involving lower terms of the $n$-solvable filtration, $\{\mathcal{F}^m_n\}$ of the string link concordance group $\mathcal{C}^m$. We utilize the Thom-Pontryagin construction to…
We prove that the $(2,1)$-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of…
The aim of this paper is to define two link invariants satisfying cubic skein relations. In the hierarchy of polynomial invariants determined by explicit skein relations they are the next level of complexity after Jones, HOMFLY, Kauffman…
In Theorem 1.2 of the paper math.GT/0002110 the author claimed to have proved that all transversal knots whose topological knot type is that of an iterated torus knot (we call them cable knots) are transversally simple. That theorem is…
The universal sl_2 invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the h-adic completed tensor powers of the quantized enveloping algebra of sl_2. In this paper, we…
Let $H$ be a diagonalizable group over an algebraically closed field $k$ of positive characteristic, and $X$ a normal $k$-variety with an $H$-action. Under a mild hypothesis, e.g. $H$ a torus or $X$ quasiprojective, we construct a certain…
We show that for any nontrivial knot $K$ and any natural number $n$ there is a diagram $D$ of $K$ such that the unknotting number of $D$ is greater than or equal to $n$. It is well known that twice the unknotting number of $K$ is less than…
We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local…