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 […]

We will examine the multiplicative structure of two skein algebras--- the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang (generated by loops and arcs).   In joint work with Chloe Marple, we found a homomorphism between the usual skein algebra for a closed torus and […]