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.
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