Related papers: State Surfaces of Links
In this note we define a polynomial invariant for colored links by a skein relation. It specializes to the Jones polynomial for classical links.
The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which…
We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and constructed the invariant P of framed links in 3-space. The invariant is closely related to the Kauffman bracket polynomial. The normalized bracket polynomial is…
It is known that the Kauffman-Murasugi-Thislethwaite type inequality becomes an equality for any (possibly virtual) adequate link diagram. We refine this condition. As an application we obtain a criterion for virtual link diagram with…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
For an oriented surface link $F$ in $\mathbb{R}^4$, we consider a satellite construction of a surface link, called a 2-dimensional braid over $F$, which is in the form of a covering over $F$. We introduce the notion of an $m$-chart on a…
Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are…
The geometry of the intermediate state (IS) flux structures of type-I superconductors, observed during early stages of magnetic flux penetration induced by an externally applied perpendicular magnetic field, is approached in terms of…
{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical…
We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered…
In this paper the author provides a generalization of classical linkage, i.e. linkage by a complete intersection, in a different context. Namely she looks at residuals in the scheme theoretic intersection of a rational normal surface or…
Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup…
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…
The study of random surfaces, especially in the asymptotics of large genus, has been of increasing interest in recent years. Many geometrical questions have analogous formulations in the theory of random graphs with a large number of…
We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree…
Surface states of a tight-binding model with nearest-neighbor hopping on a diamond lattice of finite thickness are investigated. We consider systems with (001), (110), and (111) surfaces. Even if the surface direction is fixed, there is…
We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes…