Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations

  title={Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations},
  author={Paolo Rossi},
  journal={Mathematische Annalen},
  • P. Rossi
  • Published 19 August 2008
  • Mathematics
  • Mathematische Annalen
We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of $${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}$$, i.e., the complex projective line with a orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family of (polynomial) Frobenius manifolds and integrable systems of Hamiltonian PDEs, which extend the (dispersionless) bigraded Toda hierarchy (Carlet, The extended bigraded toda hierarchy. arXiv preprint… 

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