Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string
down to long-chain molecules. The existence of knotting in a filament naturally affects its …

Rod packings in the 3‐torus encode information of some crystal structures in
crystallography. They can be viewed as links in the 3‐torus, and tools from 3‐manifold …

Rod packings are used in crystallography to describe crystal structures with linear or zigzag
chains of particles, and each rod packing can be topologically viewed as a collection of …

We present a complete table of links in the thickened torus T 2× I of complexity at most 4.
The table is constructed by the following method. First, we enumerate all abstract …

We study the relationship between knotoids and knots in the direct product of the two-
dimensional torus and an interval. Each knotoid on the sphere can be lifted to a knot of …

A knitting pattern is a tangle diagram in the square and a knitting is a tessellation of a knitting
pattern in the plane. In this paper, a classification of the knitting patterns is done in terms of …

The goal of this paper is to tabulate all prime knots in the thickened surface of genus 2
having diagrams with at most 4 crossings. First, we introduce definition of prime knot in the …

The goal of this paper is to tabulate all prime links in the thickened torus T× I having
diagrams having crossing number 5. First, we construct a table of prime projections of links …

В работе приводится полная таблица зацеплений в утолщенном торе T2× I,
минимальные диаграммы которых имеют не более 4 перекрестков. Метод построения …

We begin classification of prime knots in the thickened torus of genus 2 having diagrams
with at most 4 crossings. To this end, it is enough to construct a table of prime knot …