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Structure of the Kauffman bracket skein algebra of a surface
by
Joanna Kania-Bartoszynska
National Science Foundation
Kauffman bracket skein algebra of a surface is formed by taking linear combinations of isotopy classes of framed links in a cylinder of the surface and dividing by the relation which defines the Kauffman bracket. Multiplication comes from stacking one link over the other. Kauffman bracket skein algebras are related to the SL(2, C) characters of the fundamental group of the surface. They are used in skein theoretic constructions of topological quantum field theories. It turns out that those algebras are integral domains, and that they are Frobenius when localized over non-zero characters.
Date received: November 28, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-43.