Oriented graph-links: invariants and classification

Abstract: We consider graph-links --- combinatorial objects introduced by D.P. Ilyutko and V.O. Manturov. A graph-link is defined as an equivalence class of simple labeled graphs with respect to special transformations which play the role of Reidemeister moves. This theory naturally describes classical and virtual links up to mutation. The aim of the talk is to introduce orientation on graph-links. Further, we define some invariants of oriented graph-links and, based on these invariants, carry out a classification of oriented graph-links of low complexity (with at most $4$ vertices).

algebraic topology

Audience: researchers in the topic

Knots and representation theory