Quantum Topology / Hopf Algebra Seminar
Charles Frohman
University of Iowa
Simple diagrams and the Kauffman Bracket Skein Algebra of a Punctured Surface
Abstract: We study a basis for the Kauffman Bracket skein algebra of a finite type surface
of negative Euler characteristic, that is parametrized by admissible colorings of the edges
of an ideal triangulation of the surface. There is a filtration of the skein algebra by the weight
of diagrams, that leads to a particularly powerful expression for the product of two basis elements.
From this we prove that the Skein algebra is finitely generated, and at roots of unity it is a finite
rank module over the coordinate ring of the $SL_2\mathbb{C}$-character variety of the fundamental
group of the surface.
Tuesday January 27, 2015 at 3:00 PM in SEO 612