The structure of 2D semisimple field theories
Abstract
I classify all cohomological 2D field theories based on a semisimple complex Frobenius algebra A. They are controlled by a linear combination of kappaclasses and by an extension datum to the DeligneMumford boundary. Their effect on the GromovWitten potential is described by Givental's Fock space formulae. This leads to the reconstruction of GromovWitten invariants from the quantum cupproduct at a single semisimple point and from the first Chern class, confirming Givental's highergenus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.
 Publication:

arXiv eprints
 Pub Date:
 December 2007
 DOI:
 10.48550/arXiv.0712.0160
 arXiv:
 arXiv:0712.0160
 Bibcode:
 2007arXiv0712.0160T
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 57R56;
 14H81
 EPrint:
 Small errors corrected in v3. Agrees with published version