BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rhea Palak Bakshi (University of California\, Santa Barbara) DTSTART:20250730T160000Z DTEND:20250730T170000Z DTSTAMP:20260423T053140Z UID:TQFT/142 DESCRIPTION:Title: O n the structure of skein modules\nby Rhea Palak Bakshi (University of California\, Santa Barbara) as part of Topological Quantum Field Theory Cl ub (IST\, Lisbon)\n\n\nAbstract\nSkein modules were introduced by Józef H . Przytycki as generalisations of the Jones and HOMFLYPT polynomial link i nvariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket s kein module (KBSM) is the most extensively studied of all. However\, compu ting the KBSM of a 3-manifold is known to be notoriously hard\, especially over the ring of Laurent polynomials. With the goal of finding a definite structure of the KBSM over this ring\, several conjectures and theorems w ere stated over the years for KBSMs. We show that some of these conjecture s\, and even theorems\, are not true. In this talk I will briefly discuss a counterexample to Marche’s generalisation of Witten’s conjecture. I will show that a theorem stated by Przytycki in 1999 about the KBSM of the connected sum of two handlebodies does not hold. I will also give the exa ct structure of the KBSM of the connected sum of two solid tori and show t hat it is isomorphic to the KBSM of a genus two handlebody modulo some spe cific handle sliding relations. Moreover\, these handle sliding relations can be written in terms of Chebyshev polynomials.\n LOCATION:https://researchseminars.org/talk/TQFT/142/ END:VEVENT END:VCALENDAR