The structure of 2D semi-simple field theories

Details The structure of 2D semi-simple field theories The structure of 2D semi-simple field theories

2007-12-02

arxiv.org/abs/0712.0160v3

Mathematics

Algebraic Topology

Small errors corrected in v3. Agrees with published version

Scientific paper

10.1007/s00222-011-0352-5

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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