2007/12/31 by Constantin Teleman · 1 citation
Mathematics · Physics and Astronomy · #math.AT #math-ph #math.AG #math.MP #msc:57R56 #msc:14H81
paper · pdf · doi:10.1007/s00222-011-0352-5
Small errors corrected in v3. Agrees with published version
arxiv created 2012/02/17 · arxiv updated 2012/02/20
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.