English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We construct graph-valued analogues of the Kuperberg sl(3) and G2 invariantsfor virtual knots. The restriction of the sl(3) or G2 invariants for classicalknots coincides with the usual Homflypt sl(3) invariant and G2 invariants. Forvirtual knots and graphs these invariants provide new graphical informationthat allows one to prove minimality theorems and to construct new invariantsfor free knots (unoriented and unlabeled Gauss codes taken up to abstractReidemeister moves). A novel feature of this approach is that some knots are ofsufficient complexity that they evaluate themselves in the sense that theinvariant is the knot itself seen as a combinatorial structure. The papergeneralizes these structures to virtual braids and discusses the relationshipwith the original Penrose bracket for graph colorings.

Graphical Constructions for the sl(3), so(3) and G2 Invariants for Virtual Knots, Virtual Braids and Free Knots