Related papers: Link concordance, boundary link concordance and et…
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 introduce the $SU(N)$ Casson-Lin invariants for links $L$ in $S^3$ with more than one component. Writing $L = \ell_1 \cup \cdots \cup \ell_n$, we require as input an $n$-tuple $(a_1,\ldots, a_n) \in {\mathbb Z}^n$ of labels, where $a_j$…
In this paper we conjecture that the Links-Gould invariant of links, that we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular it seems to give a lower bound for the genus of…
To each link $L$ in $S^3$ we associate a collection of certain labelled directed trees, called width trees. We interpret some classical and new topological link invariants in terms of these width trees and show how the geometric structure…
Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally…
In 1999, Rozansky conjectured the existence of a rational presentation of the Kontsevich integral of a knot. Roughly speaking, this rational presentation of the Kontsevich integral would sum formal power series into rational functions with…
Let $L$ be an alternating prime non-split link in $S^3$. We use the category of flypes between reduced alternating diagrams for $L$ to classify involutions on $L$. As consequences, we show that the quotient of an alternating periodic link…
The link invariant, arising from the cyclic quantum dilogarithm via the particular $R$-matrix construction, is proved to coincide with the invariant of triangulated links in $S^3$ introduced in R.M. Kashaev, Mod. Phys. Lett. A, Vol.9 No.40…
A delta-move is a local move on a link diagram. The delta-Gordian distance between links measures the minimum number of delta-moves needed to move between link diagrams. A self delta-move only involves a single component of a link whereas a…
It has been conjectured that the algebraic crossing number of a link is uniquely determined in minimal braid representation. This conjecture is true for many classes of knots and links. The Morton-Franks-Williams inequality gives a lower…
We construct the concordance invariant coming from the $E(-1)$ spectral sequence on Khovanov homology in the same way Rasmussen's $s$ invariant comes from the Lee spectral sequence, and show that it gives a bound on the nonorientable slice…
A rational link may be represented by any of the (infinitely) many link diagrams corresponding to various continued fraction expansions of the same rational number. The continued fraction expansion of the rational number in which all signs…
In 2007, Cochran-Friedl-Teichner gave sufficient conditions for when a multi-infection link is topologically slice involving a Milnor's invariant condition on the infecting string link. In this paper, we give a different Milnor's invariant…
As proved by Hedden and Ording, there exist knots for which the Ozsvath-Szabo and Rasmussen smooth concordance invariants, tau and s, differ. The Hedden-Ording examples have nontrivial Alexander polynomials and are not topologically slice.…
Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual…
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,…
A link is called $\chi-$slice if it bounds a smooth properly embedded surface in the 4-ball with no closed components and Euler characteristic 1. If a link has a single component, then it is $\chi-$slice if and only if it is slice. One…
We submit a new way to detect pairs of non-cobordant surface-links. We find a new example of a pair of non-cobordant surface-links with the following properties: Orr invariant, Cochran sequence, Sato-Levine invariant, the alinking number…
This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.
We define an integer valued invariant for two-component links in S^3 by counting projective SU(2) representations of the link group having non-trivial second Stiefel-Whitney class. We show that our invariant is, up to sign, the linking…