Related papers: On alternating quasipositive links

Let $H$ be a cubic graph admitting a 3-edge-coloring $c: E(H)\to \mathbb Z_3$ such that the edges colored by 0 and $\mu\in\{1,2\}$ induce a Hamilton circuit of $H$ and the edges colored by 1 and 2 induce a 2-factor $F$. The graph $H$ is…

In this paper, we are motivated by two conjectures proposed by C. Bender et al.\ in 2024, which have remained open questions. The first conjecture states that if the complemented zero-divisor graph \( G(S) \) of a commutative semigroup \( S…

Let $D$ be a reduced alternating diagram of a non-split link $L$ and $\tilde{L}$ be the link whose diagram is obtained from $D$ by a crossing change. If $\tilde{L}$ is alternating, then $c(\tilde{L})\leq c(L)-2$. In this paper we explore…

We prove a Landis type unique continuation result for positive quasi-linear operators on graphs. Specifically, we give decay criteria that ensures when a harmonic function for a positive quasilinear Schr\"odinger operator with potential…

We prove that the Jones diameter of a link is twice its crossing number whenever the breadth of its Jones polynomial equals the difference between the crossing number and the Turaev genus. This implies that such link is adequate, as per the…

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…

It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link can be cancelled up to link homotopy in a (componentwise) connected sum with another link. In this paper we address the question whether…

Using a new tool called lassos, we establish a new correspondence between cellular link {diagrams} on closed surfaces and equivalence classes of virtual link {diagrams}. This is analogous to a well-known correspondence among the links…

It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is 1. We extend this result to almost positive links and partly identify the 3 following coefficients for…

The main purpose of this paper is to provide a structure theorem for codimension one singular transversely projective foliationson projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank two…

We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.

We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almost complex 4-manifold with many curves admits a taming…

Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…

Let A be a basic connected finite dimensional algebra over an algebraically closed field. Assuming that A is quasitilted, we prove that A is simply connected if and only if its first Hochschild cohomology group HH^1(A) vanishes. This…

Tait's flyping conjecture, stating that two reduced, alternating, prime link diagrams can be connected by a finite sequence of flypes, is extended to reduced, alternating, prime diagrams of 4-regular graphs in S^3. The proof of this version…

We consider bi-linear analogues of $s$-positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite…

We extend a result of Thistlethwaite [17, Theorem 1(iv)] on the structure of the Jones polynomial of alternating links to the wider class of quasi-alternating links. In particular, we prove that the Jones polynomial of any prime…

We show some properties of a Seifert matrix of an $n$-component Brunnian link. In particular, we give a necessary and sufficient condition for a matrix to be a Seifert matrix of a 2-component Brunnian link up to S-equivalence.

A simple topological graph is $k$-quasiplanar ($k\geq 2$) if it contains no $k$ pairwise crossing edges, and $k$-planar if no edge is crossed more than $k$ times. In this paper, we explore the relationship between $k$-planarity and…

We present a semiclassical theory of current correlations in multiterminal chaotic dot-superconductor junctions, valid in the absence of the proximity effect in the dot. For a dominating coupling of the dot to the normal terminals and a…