We welcome all undergraduate\/graduate students and faculty to attend topology seminar!<\/p>\n
Speaker: Rhea Palak Bakshi (University of California Santa Barbara)<\/p>\n
Title: The skein module of the connected sum of two copies of L(0,1)<\/p>\n
Abstract: Abstract: Skein modules were introduced by Jozef H. Przytycki, and independently by Vladmimor Turaev, as generalisations of the Jones, Kauffman bracket, and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However, computing the KBSM of a 3-manifold is known to be notoriously hard, especially over the ring of Laurent polynomials. Marche conjectured that over the ring of Laurent polynomials, the KBSM of closed oriented 3-manifolds splits into the sum of free and torsion modules. The counterexample to this conjecture is given by the connected sum of two copies of the real projective space. With the goal of finding a definite structure of the KBSM over this ring, we compute the skein module of S^1 x S^2 # H_1 and S^1 x S^2 # S^1 x S^2. We show that it is isomorphic to the KBSM of a genus two handlebody modulo some specific handle sliding relations. Moreover, these handle sliding relations can be written in terms of Chebyshev polynomials. We also discuss whether the KBSM of these manifolds splits into the sums of free and torsion modules. This is joint work with Seongjeong Kim, Shangjun Shi, and Xiao Wang.<\/p>\n","protected":false},"excerpt":{"rendered":"
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