Related papers: Dislocations of arbitrary topology in Coulomb eige…
We prove that, given any finite link L in R^3, there is a high energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of…
The complex eikonal equation in $(3+1)$ dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the…
Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and links. For example, for Pixton diffeomorphisms, the…
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of…
Semiholomorphic polynomials are functions $f:\mathbb{C}^2\to\mathbb{C}$ that can be written as polynomials in complex variables $u$, $v$ and the complex conjugate $\overline{v}$. We prove the semiholomorphic analogoue of Akbulut's and…
The Hessian Topology is a subject with interesting relations with some classical problems of analysis and geometry. In this article we prove a conjecture on this subject stated by V.I. Arnold concerning the number of connected components of…
Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for…
We establish a natural identification of cobordism classes of framed links with the fundamental group of the group-completed configuration space of points in the plane, by appeal to Okuyama's previously underappreciated interval…
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that…
We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the…
This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…
We provide the first complete computations of colored sl(N) homology for a nontrivial knot. In doing so, we show that the colored sl(N) homology of the trefoil labeled by an exterior power of the defining representation is isomorphic to the…
Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent…
We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…
We explore the topological properties of non-Hermitian nodal-link semimetals with dissipative cold atoms in a three-dimensional optical lattice. We construct a two-band continuum model in three dimensions with a spin-dependent gain and…
We discovered that abnormal Mott physics can emerge even in weakly correlated 4f fermions through their interplay with topological singularity. Employing ab initio many-body perturbation theory combined with dynamical mean field theory, we…
A handlebody-knot is a handlebody embedded in the 3-sphere. We establish a uniform method to construct invariants for handlebody-links. We introduce the category $\mathcal{T}$ of handlebody-tangles and present it by generators and…
Hopf-link semimetals exhibit exotic gapless band structures with fascinating topological properties, which have never been observed in nature. Here we demonstrate nodal lines with topological form of Hopf-link chains in artificial…
A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…
Link/knot invariants are series with integer coefficients, and it is a long-standing problem to get them positive and possessing cohomological interpretation. Constructing positive "superpolynomials" is not straightforward, especially for…