2010/01/03 by Denis Petrovich Ilyutko, Vassily Olegovich Manturov, Ilyutko, Denis Petrovich +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.1001.0384
32 pages, 21 figures
arxiv created 2010/01/03 · openalex publication_date 2010/01/03 · arxiv updated 2010/01/14 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. In this paper we show how some methods of classical and virtual knot theory can be translated into the language of abstract graphs, and some theorems can be reproved and generalised to this graphical setting. We construct various invariants, prove certain minimality theorems and construct functorial mappings for graph-knots and graph-links. In this paper, we first show non-equivalence of some graph-links to virtual links.