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pro vyhledávání: '"Korablev, Philipp"'
Autor:
Korablev, Philipp
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 diagram. Later, in 2020, Anastasiya Galkina generalised this invariant
Externí odkaz:
http://arxiv.org/abs/2408.04510
Autor:
Korablev, Philipp
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 express it in algebraic form as a family of equations with a set of l
Externí odkaz:
http://arxiv.org/abs/2402.16682
Autor:
Korablev, Philipp
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 invariants for links coloured by quandles.
Externí odkaz:
http://arxiv.org/abs/2311.03871
Autor:
Korablev, Philipp
Publikováno v:
Siberian Electronic Mathematical Reports. 2022. Vol. 19, no. 2. PP. 698-707
A homologically trivial part of any Turaev-Viro invariant odd order $r$ is a Turaev-Viro type invariant order $\frac{r + 1}{2}$. In this paper we find an explicit formulas for this Turaev -- Viro type invariant, corresponding to the invariant order $
Externí odkaz:
http://arxiv.org/abs/2310.05802
Autor:
Korablev, Philipp
In the paper we introduce the construction of invariants for 3-manifolds, based on the same key concepts as the classical Dijkgraaf-Witten invariant. We introduce the notion of a special $G$-system and describe how each system induces the invariant n
Externí odkaz:
http://arxiv.org/abs/2305.00737
Autor:
Korablev, Philipp
We describe the simplest non-trivial modular category $\mathfrak{E}$ with two simple objects. Then we extract from this category the invariant for non-oriented links in 3-sphere and two invariants for 3-manifolds: the complex-valued Turaev - Reshetik
Externí odkaz:
http://arxiv.org/abs/2305.00733
Autor:
Korablev, Philipp, Tarkaev, Vladimir
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 a knotoid are the crossing number and the height. The latter is the le
Externí odkaz:
http://arxiv.org/abs/2009.02718
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