Related papers: Doubly slice Montesinos links

Recently Swatee Naik and Theodore Stanford proved that two S-equivalent knots are related by a finite sequence of doubled-delta moves on their knot diagrams. We show that classical S-equivalence is not sufficient to extend their result to…

We give applications of the higher Lefschetz theorems for foliations of [BH10], primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information.…

The $L$-space conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an $L$-space, having a left-orderable fundamental group, and admitting a co-oriented taut foliation. We investigate these properties for…

We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant…

In this article we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not $L$-spaces, if and only if it is not an $ADE$ link up to…

We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and…

We prove that if a knot $K$ has a particular type of diagram then all non-trivial surgeries on $K$ contain a coorientable taut foliation. Knots admitting such diagrams include many two-bridge knots, many pretzel knots, many Montesinos knots…

We present a systematic and detailed study of the robustness of directed networks under random and targeted removal of links. We work with a set of network models of random and scale free type, generated with specific features of clustering…

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…

We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quasi-positive, positive, or the closure of a positive braid. The main applications of our results are a characterisation of positive links with…

According to the decomposition and relative hard Lefschetz theorems, given a projective map of complex quasi projective algebraic varieties and a relatively ample line bundle, the rational intersection cohomology groups of the domain of the…

We develop a method to show the fundamental group of the double branched covering of a link is not left-orderable by introducing the notion of the coarse presentation. As in the usual group presentations, a coarse presentation is given by a…

A manifold $M$ is said to be a double disk bundle if it can be decomposed as a union of two disk bundles glued together by a diffeomorphism of their boundaries. We show that if $M^n$ is a closed simply connected $n$-manifold with $n$ even…

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…

The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

Double twist knots $K_{m, n}$ are known to be rationally slice if $mn = 0$, $n = -m\pm 1$, or $n = -m$. In this paper, we prove the converse. It is done by showing that infinitely many prime power-fold cyclic branched covers of the other…

We prove that certain fibered, $-$amphicheiral knots are rationally slice. Moreover, we show that the concordance invariants $\nu^+$ and $\Upsilon(t)$ from Heegaard Floer homology vanish for a class of knots that includes rationally slice…

A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…