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Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds. (English) Zbl 1062.53073
In the paper under review the authors study how Gromov-Witten invariants of Calabi-Yau 3-folds can be transformed under symplectic surgery. Another outcome of the paper is given by the relation between the naturality problem of quantum cohomology and birational geometry. This relation is both surprising and intriguing.

MSC:
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
32Q65 Pseudoholomorphic curves
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