The forbidden quiver of a link (Sam Nelson, CMC)

Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the knot or link — indeed, virtual knots are all trivial if we allow forbidden moves. However, virtual links remain non-trivial. In this talk we show how to think of these links as quivers and in the process, define several polynomial invariants of link homotopy. This is joint work with Stella Shah (Scripps College).