Skein algebra of surfaces

Thang Le (Georgia Tech)

Abstract: The skein module of a 3-manifold M is defined using links embedded M and is intimately related to the Jones polynomial. For a thicken surface the module has a natural algebra structure. When the surface bounds a 3-manifold, the skein algebra of the surface acts on the skein module of the 3-manifold. This geometric action is used in constructions of topological quantum field theories. We will discuss the structure of the skein algebra of a surface, its relations to quantum tori, and faithfulness of the geometric action.