Gauss diagram formulas of Vassiliev invariants of spatial 2-bouquet graphs
Noboru Ito, Natsumi Oyamaguchi
TL;DR
This paper introduces the first simple Gauss diagram formulas for Vassiliev invariants of spatial 2-bouquet graphs, which are equivalent to 2-string links, expanding the understanding of these invariants.
Contribution
It provides the first explicit Gauss diagram formulas for Vassiliev invariants of spatial 2-bouquet graphs, filling a gap in knot theory.
Findings
New formulas for Vassiliev invariants of spatial 2-bouquet graphs
Equivalence of these invariants to 2-string links
First known Gauss diagram formulas for this class
Abstract
We introduce new formulas that are Vassiliev invariants of flat vertex isotopy classes of spatial 2-bouquet graphs, which are equivalent to 2-string links. Although any Gauss diagram formula of Vassiliev invariants of spatial 2-bouquet graphs in a 3-space has been unknown, this paper gives the first and simple example.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Advanced Graph Theory Research