Bernd Siebert
Schriftzug: Fachbereich Mathematik 
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Forschungsseminar: Komplexe Geometrie

05.04.2013 Dr. Oliver Fabert (Univ. Freiburg)

Classical mirror symmetry for open Calabi-Yau manifolds

Abstract: The classical mirror symmetry conjecture for closed Calabi-Yau manifolds can be formulated as an isomorphism of Frobenius manifolds, involving the Frobenius manifold structure on quantum cohomology given by the Gromov-Witten invariants on the symplectic side. Passing from closed to open symplectic manifolds, it is known that quantum cohomology needs to be replaced by symplectic cohomology, defined using Floer theory. Generalizing the closed case, I show that the symplectic cohomology of an open symplectic manifold can be equipped with the structure of a cohomology F-manifold, a differential graded version of a Frobenius manifold. Since this indeed fits nicely with the expectations from mirror symmetry, I will formulate a classical mirror symmetry conjecture for open Calabi-Yau manifolds.


 
  Seitenanfang  Impressum 2013-04-01, Bernd Siebert