Related papers: Knotted Configurations with Arbitrary Hopf Index f…
We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of…
We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D66, 041701(R) (2002)] that certain modification of the ordinary model…
The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with distinct topology from the underlying parameter space. Spectral topology permits parametric loops to map the affiliated eigenvalue…
We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. Indeed, any monoidal adjunction between autonomous…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The…
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter…
We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…
In this paper, we study the realizability problem for retarded functional differential equations near an equilibrium point undergoing a nonlinear mode interaction between a saddle-node bifurcation and a non-resonant multiple Hopf…
We relate certain abelian invariants of a knot, namely the Alexander polynomial, the Blanchfield form, and the Arf invariant, to intersection data of a Whitney tower in the 4-ball bounded by the knot. We also give a new 3-dimensional…
The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and…
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…
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there…
Nonresonant Hopf-Hopf singularity in neutral functional differential equation (NFDE) is considered. An algorithm for calculating the third-order normal form is established by using the formal adjoint theory, center manifold theorem and the…
Witten's approach to Khovanov homology of knots is based on the five-dimensional system of partial differential equations, which we call Haydys-Witten equations. We argue for a one-to-one correspondence between its solutions and solutions…
A family of deformed models of the sine-Gordon-type can be generated by twisting the sine-Gordon model. As a particular case, the 3-sine-Gordon model is here addressed, whose differential configurational entropy and the differential…
Three-dimensional stationary precession solitons with nonzero Hopf indices are found numerically by solving the Landau-Lifshitz equation. The structure and existence domain of the solitons are found.
We construct new knot polynomials. Let $V$ be the standard solid torus in 3-space and let $pr$ be its standard projection onto an annulus. Let $M$ be the space of all smooth oriented knots in $V$ such that the restriction of $pr$ is an…