Holonomicity of skein modules

Iordanis Romaidis (University of Edinburgh)

Wednesday 4th February 16:00-17:00
Maths 311B

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, finiteness is replaced by holonomicity over the boundary skein algebra. Roughly, a module is holonomic if it is finitely generated and has a Lagrangian support. I will introduce the background from skein theory and deformation quantization needed to state the main theorem. Finally, if time permits, I will discuss aspects of the proof and applications to other finiteness properties of skein modules. 

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