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arXiv · 1508.05922

Edge contraction on dual ribbon graphs and 2D TQFT

Olivia Dumitrescu·Motohico Mulase
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Abstract

We present a new set of axioms for 2D TQFT formulated on the category of cell graphs with edge-contraction operations as morphisms. We construct a functor from this category to the endofunctor category consisting of Frobenius algebras. Edge-contraction operations correspond to natural transformations of endofunctors, which are compatible with the Frobenius algebra structure. Given a Frobenius algebra A, every cell graph determines an element of the symmetric tensor algebra defined over the dual space A*. We show that the edge-contraction axioms make this assignment depending only on the topological type of the cell graph, but not on the graph itself. Thus the functor generates the TQFT corresponding to A.

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BibTeXRIS

Olivia Dumitrescu, Motohico Mulase. 2017-09-30. Edge contraction on dual ribbon graphs and 2D TQFT. https://arxiv.org/abs/1508.05922

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