Relationships between skein algebras (Helen Wong, CMC)

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 the Roger-Yang skein algebra for a twice-punctured annulus.   In this talk, I’ll present some ways we used that homomorphism to do computations, and whether there might be similar relationships between skein algebras of other surfaces.