Claremont Topology Seminar: Robert Bowden (HMC)

Title: Chebyshev Threadings in Skein Algebras for Punctured Surfaces

Abstract: Skein algebras are algebras of links in a surface quotiented by diagram-based equivalence relations based on the Kauffman bracket. In the case of surfaces with punctures, the skein algebra is generated by links as well as arcs between the punctures, and there are additional skein relations for the arcs. We examine the algebraic structure of the punctured case, finding a description of the central elements at certain roots of unity. Our construction is closely related to the one for the usual skein algebra, where central elements come from threading links by Chebyshev polynomials.