Holonomic skein modules

Abstract: For a reductive group G and a quantum parameter q, skein theory assigns skein algebras to surfaces and skein modules to 3-manifolds. Skein modules of closed 3-manifolds at generic q were conjectured by Witten to be finite-dimensional—a statement later proved by Gunningham, Jordan, and Safronov. In this talk, I will present joint work with David Jordan on a generalization of this conjecture to 3-manifolds with boundary. In this setting, the finiteness property is replaced by the condition that the skein module is holonomic over the boundary skein algebra. Roughly, a module is holonomic if it is finitely generated and has a Lagrangian support. We prove holonomicity for skein modules of GL2 and SL2​ by constructing transfer bimodules, and proving holonomicity preservation theorems analogous to those in the classical theory of D-modules.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home