The structure of 2D semi-simple field theories

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.

Small errors corrected in v3. Agrees with published version

References in corpus (8)

• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Relations between the correlators of the topological sigma-model coupled to gravity
• Wheeled PROPs, graph complexes and the master equation
• Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map
• Semisimple Quantum Cohomology and Blow-ups
• Symmetries of WDVV equations
• An update on semisimple quantum cohomology and F-manifolds

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