Topological Strings and $D$-Branes

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In this talk we give a brief review of the algebraic structure behind the open and closed topological strings and $D$-branes and emphasize the role of tensor category and the Frobenius algebra. Also, we speculate on the possibility of generalizing the topological strings and the $D$-branes through the subfactor theory.
Prepared for the Second International Conference on Fundamental Interactions, June 6-12, 2004, Pedra Azul, Espirito Santo, Brazil

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