Finiteness for Skein Modules
Talk by Dr. Sam Gunningham (Dept of Mathematical Sciences/MSU and University of Edinburgh, UK)
03/15/2021 Zoom Meeting
The skein module of a 3-dimensional manifold is a vector space generated by embedded knots modulo certain "skein relations". Skein modules were first defined about 30 years ago independently by Przytycki and Turaev, and have been extensively studied in the subsequent years. They are notoriously hard to compute! Remarkably, the question of their finite dimensionality only began to circulate amongst the skein community in around 2015, prompted by a suggestion of Witten. In joint work with David Jordan and Pavel Safronov from 2019, we show that the skein module of a closed 3-manifold is finite dimensional (for generic parameters), confirming Witten's conjecture.
In this talk I will motivate and define the skein module before explaining some aspects of what goes into our proof. No prior familiarity with 3-manifolds or knots will be assumed.