Skein modules of closed 3-manifolds

Abstract: The Kauffman bracket skein module of a 3-manifold M is a Q(A)-vector space, describing the combinatorics of links in M up to some local relations. Computing the skein module of a given 3-manifold has long been a hard question and besides a few examples, no general algorithm is known. However a recent conjecture of Witten, now proven non constructively by Gunningham, Jordan and Safronov, states that the skein module of a closed 3-manifold is finite dimensional. After discussing the motivations behind the conjecture and some open questions, we will present some joint work with Maxime Wolff, describing explicitly the skein module of the product of a surface and a circle.

HEP - theorymathematical physicsalgebraic geometryalgebraic topologycombinatoricsdifferential geometrygeometric topologyquantum algebra

Audience: researchers in the topic

Algebra, Geometry and Physics seminar (MPIM Bonn/HU Berlin)

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