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Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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Frobenius modules and essential surface cobordisms
by
Masahico Saito
University of South Florida
Coauthors: J. Scott Carter

A formulation of an algebraic structure is proposed, that describes essential surface cobordisms in 3-manifolds. It is a refinement of (1+1)-TQFTs, and has module and comodule structures over a Frobenius algebra with additional conditions. This structure gives a unified algebraic view of the differentials of a generalization of Khovanov homology defined by Asaeda-Przytycki-Sikora for thickened surfaces and those defined by Ishii-Tanaka for virtual knots. Constructions of new examples are also discussed.

Date received: November 30, 2008

Copyright © 2008 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 # caxq-44.