Title: Skein modules and perverse sheaves.
Abstract: The skein module of a 3-manifold is a certain vector space spanned by embedded links (or graphs), modulo certain relations depending on a quantum parameter. When the quantum parameter is set to 1, the skein module is identified with the ring of functions on the character variety of M. On the other hand, when the quantum parameter is generic, the skein module of a closed 3-manifold turns out to be finite dimensional. In this talk I will survey some ongoing work with Pavel Safronov, in which we realize the skein module of a closed 3-manifold at generic quantum parameter in terms of the cohomology of a certain perverse sheaf on its character variety. This work is part of a larger program with Safronov, Jordan, and Ben-Zvi to study the Kapustin--Witten geometric Langlands TQFT on 3-manifolds.
Noah Riggenbach
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