Classification of Knots in a Thickened Torus with Minimal Octahedron Diagrams which are not Contained in an Annulus
Authors
Alena Andreevna Akimova
Chelyabinsk State University
Keywords:
knot, thickened torus, knot table
Abstract
The aim of this research is to tabulate knots in a thickened torus T×I having minimal diagrams which are not contained in an annulus and correspond to the octahedron graph. Tabulation consists of three steps. First, a table of knot projections on T was compiled. Then, every projection was converted into a set of corresponding diagrams. Finally, using a generalized version of the Kauffman bracket as an invariant, duplicates were removed and all the knots obtained were proved to be different.
Author Biography
Alena Andreevna Akimova, Chelyabinsk State University
Post-graduate Student, South Ural State University; Laboratory of Quantum Topology, Chelyabinsk State University
