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Algebraic Structures Derived from Foams and TQFTs
by
Masahico Saito
University of South Florida
Coauthors: Scott Carter
Foams are surfaces with branch lines at which three sheets merge. The 2D TQFT of surfaces is characterized by means of Frobenius algebras, where saddle points correspond to multiplication and comultiplication. In this talk, we explore algebraic operations that branch lines derive under TQFT. In particular, we point out that Lie bracket and bialgebra structures can be found in infinitely many examples. Relations to the original Frobenius algebra structures are discussed both algebraically and diagrammatically. Foam skein modules of 3-manifolds are defined. Progresses made after the AMS Boca Raton meeting will be discussed.
Date received: November 19, 2009
Copyright © 2009 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 # cazp-09.