The wrapped Fukaya category for semi-toric Calabi–Yau

Yoel Groman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce the wrapped Donaldson–Fukaya category of a (generalized) semi-toric SYZ fibration with Lagrangian section satisfying a tameness condition at infinity. Examples include the Gross fibration on the complement of an anti-canonical divisor in a toric Calabi–Yau 3-fold. We compute the wrapped Floer cohomology of a Lagrangian section and find that it is the algebra of functions on the Hori–Vafa mirror. The latter result is the key step in proving homological mirror symmetry for this case. The techniques developed here allow the construction in general of the wrapped Fukaya category on an open Calabi–Yau manifold carrying an SYZ fibration with nice behavior at infinity. We discuss the relation of this to the algebraic vs analytic aspects of mirror symmetry.

Original languageEnglish
Pages (from-to)2373-2439
Number of pages67
JournalJournal of the European Mathematical Society
Issue number7
StatePublished - 2024

Bibliographical note

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© 2024 European Mathematical Society.


  • Fukaya category
  • symplectic cohomology


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