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Explore the intricacies of skein modules in this 54-minute lecture by Rhea Palak Bakshi from ETH Zurich, presented at the Banach Center. Delve into the world of Kauffman bracket skein modules (KBSM) and their significance as generalizations of Jones and HOMFLYPT polynomial link invariants in 3-manifolds. Discover the challenges in computing KBSMs over the ring of Laurent polynomials and examine the evolution of conjectures and theorems surrounding their structure. Learn about a counterexample to Marche's generalization of Witten's conjecture and understand why Przytycki's 1999 theorem on the KBSM of connected sum handlebodies does not hold. Gain insights into the exact structure of the KBSM for the connected sum of two solid tori and its isomorphism to the KBSM of a genus two handlebody, with a focus on specific handle sliding relations expressed using Chebyshev polynomials.
