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The Localized Skein Algebra is Frobenius
by
Charles Frohman
The University of Iowa
Coauthors: Nelson Abdiel Cólon Vargas
When A in the Kauffman bracket skein relation is a primitive 2Nth root of unity, where N ≥ 3 is odd,
the Kauffman bracket skein algebra KN(F) of a finite type surface F is a ring extension of
the SL2C-characters χ(F) of the fundamental group of F. We localize by inverting the nonzero characters
to get an algebra S-1KN(F) over the function field of the character variety. We prove the algebra S-1KN(F)
is a symmetric Frobenius algebra. Along the way we prove K(F) is finitely generated, KN(F) is a finite rank module
over χ(F), and threaded primitive diagrams are units in S-1KN(F).
Date received: December 27, 2014
Copyright © 2014 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 # cbjz-75.