The partition function of a topological field theory

  title={The partition function of a topological field theory},
  author={Kevin J. Costello},
  journal={Journal of Topology},
  • K. Costello
  • Published 2009
  • Mathematics
  • Journal of Topology
This is the sequel to my paper ‘TCFTs and Calabi–Yau categories’, Advances in Mathematics 210 (2007) no. 1, 165–214. Here we extend the results of that paper to construct, for certain Calabi–Yau A∞ categories, something playing the role of the Gromov–Witten potential. This is a state in the Fock space associated to periodic cyclic homology, which is a symplectic vector space. Applying this to a suitable A∞ version of the derived category of sheaves on a Calabi–Yau yields the B model potential… 

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