On ribbon graphs and virtual links
Scott Baldridge, Louis H. Kauffman, William Rushworth
TL;DR
This paper establishes a new correspondence between decorated ribbon graphs and virtual links, enabling the transfer of invariants between these two mathematical structures.
Contribution
It introduces a novel equivalence relation on ribbon graphs that directly corresponds to virtual links, facilitating cross-application of invariants.
Findings
New equivalence relation on decorated ribbon graphs
Correspondence between ribbon graphs and virtual links
Method to convert invariants between the two structures
Abstract
We introduce a new equivalence relation on decorated ribbon graphs, and show that its equivalence classes directly correspond to virtual links. We demonstrate how this correspondence can be used to convert any invariant of virtual links into an invariant of ribbon graphs, and vice versa.
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