On the counting of holomorphic discs in toric Fano manifolds

Details On the counting of holomorphic discs in toric Fano manifolds On the counting of holomorphic discs in toric Fano manifolds

2006-04-24

arxiv.org/abs/math/0604502v3

Mathematics

Symplectic Geometry

16 pages, 4 figures, rewritten using the language of cyclic A-infinity algebra

Scientific paper

We first compute three-point open Gromov-Witten numbers of Lagrangian torus fibers in toric Fano manifolds, and show that they depend on the choice of three points, hence they are not invariants. We show that for a cyclic A-infinity algebras, such counting may be defined up to Hochschild or cyclic boundary elements. In particular we obtain a well-defined function on Hochschild or cyclic homology of a cyclic A-infinity algebra, which has an invariance property under cyclic A-infinity homomorphism.

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