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arXiv · 0712.0160

The structure of 2D semi-simple field theories

Constantin Teleman
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Abstract

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.

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BibTeXRIS

Constantin Teleman. 2012-02-17. The structure of 2D semi-simple field theories. https://doi.org/10.1007/s00222-011-0352-5

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