5 papers
Quadrangulation moves
Philipp Korablev
We prove that any two quadrangulations of the same surface, i.e., decompositions of a surface into squares, can be transformed into one another by a finite sequence of two-dimensio…
Electric group for knots and links
Philipp Korablev
In 2014 Andrey Perfiliev introduced the so-called electric invariant for non-oriented knots. This invariant was motivated by using Kirchhoff's laws for the dual graph of the knot d…
Pentagon relation and Biedenharn-Elliott identity
Philipp Korablev
The main subject of the paper is the pentagon relation. This relation can be expressed in different ways. We start with the natural geometric form of the pentagon relation. Then we…
Hierarchical quandles
Philipp Korablev
We introduce the notion of a hierarchical quandle, which is a generalisation of diquandles and multi-quandles. Using hierarchical quandle colourings, we construct a cocycle invaria…
A relation between the crossing number and the height of a knotoid
Philipp Korablev, Vladimir Tarkaev
Knotoids are open ended knot diagrams regarded up to Reidemeister moves and isotopies. The notion is introduced by V.~Turaev in 2012. Two most important numeric characteristics of…