Categorical primitive forms of Calabi–Yau A∞-categories with semi-simple cohomology

• Lino Amorim ^[1] ; Junwu Tu ^[2]
  1. [1] Kansas State University

     Kansas State University

     City of Manhattan, Estados Unidos

     
  2. [2] ShanghaiTech University

     ShanghaiTech University

     China

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
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• Resumen

  • We study categorical primitive forms for Calabi–Yau A∞ categories with semi-simple Hochschild cohomology. We classify these primitive forms in terms of certain grading operators on the Hochschild homology. We use this result to prove that, if the Fukaya category Fuk(M) of a symplectic manifold M has semi-simple Hochschild cohomology, then its genus zero Gromov–Witten invariants may be recovered from the A∞-category Fuk(M) together with the closed-open map. An immediate corollary of this is that in the semi-simple case, homological mirror symmetry implies enumerative mirror symmetry.