Skein theory forms a once-categorified 3d TQFT and assigns skein algebras to surfaces and skein modules to 3-manifolds. Motivated by physics, these modules are expected to satisfy a certain holonomicity property, generalizing Witten's finiteness conjecture of skein modules. In this talk, we will recall the basic notions of skein theory as a deformation quantization theory, and then state and discuss the generalized Witten's finiteness conjecture.
Ben Webster, Wenjun Niu