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Quantum cohomology of the Grassmannian and alternate Thom-Sebastiani. (English) Zbl 1151.53075
Authors’ abstract: We introduce the notion of an alternate product of Frobenius manifolds and we give, after I. Ciocan-Fontanine and the authors [Invent. Math. 171, No. 2, 301–343 (2008; Zbl 1164.14012)], an interpretation of the Frobenius manifold structure canonically attached to the quantum cohomology of $$G(r,n+1)$$ in terms of alternate products. We also investigate the relationship with the alternate Thom-Sebastiani product of Laurent polynomials.

##### MSC:
 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 14M15 Grassmannians, Schubert varieties, flag manifolds
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