Related papers: Mechanical Normal Forms of Knots and Flat Knots

In the loop representation the quantum constraints of gravity can be solved. This fact allowed significant progress in the understanding of the space of states of the theory. The analysis of the constraints over loop dependent wavefunctions…

It has been argued based on electric-magnetic duality that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four-dimension. And the Euler characteristic of…

This paper reports an experiment about abnormal deflection of cathode-ray in odd-symmetric magnetic field. The measurement results show that during cathode-ray passes through odd-symmetric magnetic field, a deflection opposite to Lorentz…

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…

There is a positive constant $c_1$ such that for any diagram $D$ representing the unknot, there is a sequence of at most $2^{c_1 n}$ Reidemeister moves that will convert it to a trivial knot diagram, $n$ is the number of crossings in $D$. A…

The binding energies of deformed even-even nuclei have been analysed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner - Kirkwood $\hbar$ expansion up to fourth - order, instead…

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly…

The present paper has a number of distinct purposes. First is to give a description of a class of electromagnetic knots from the perspective of foliation theory. Knotted solutions are then interpreted in terms of two codimension-2…

Consider a continuous flow in $\mathbb{R}^3$ or any orientable $3$-manifold. Let $(Q_1, Q_0)$ be an index pair in the sense of Conley and consider the region $N := \overline{Q_1 - Q_0}$. (An example of this is a compact $3$-manifold $N$…

Using a combination of the replica-exchange Monte Carlo algorithm and the multicanonical method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudo-phase…

This paper contains the first knot polynomials which can distinguish the orientations of classical knots and which make no excplicit use of the knot group. But they make extensive use of the meridian and of the longitude in a geometric way.…

For a knot $K$ with $\Delta_K(t)\doteq t^2-3t+1$ in a homology $3$-sphere, let $M$ be the result of $2/q$-surgery on $K$. We show that an appropriate assumption on the Reidemeister torsion of the universal abelian covering of $M$ implies…

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behaviour is of unsteady, irregular…

We quantize a particle confined to move on a torus knot satisfying constraint condition ($p \theta + q \phi) \approx 0$, within the context of a geometrically motivated approach - the Faddeev-Jackiw formalism. We also deduce the constraint…

Knotoid theory is a generalization of knot theory introduced by Turaev in 2012. In recent years, various invariants of knotoids have been studied. In this paper, we mainly discuss unknotting moves and unknotting numbers of plus-welded…

We observe that any knot invariant extends to virtual knots. The isotopy classification problem for virtual knots is reduced to an algebraic problem formulated in terms of an algebra of arrow diagrams. We introduce a new notion of finite…

We give empirical evidence that the UV-divergences of a renormalizable field theory are knot invariants.

We construct many examples of non-slice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional…

In previous papers, the author realized the following principle for many knot theories: if a knot diagram is complicated enough then it reproduces itself, i.e., is a subdiagram of any other diagram equivalent to it. This principle is…

Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…