Counting pseudo-holomorphic discs in Calabi-Yau 3 fold

Details Counting pseudo-holomorphic discs in Calabi-Yau 3 fold Counting pseudo-holomorphic discs in Calabi-Yau 3 fold

2009-08-02

arxiv.org/abs/0908.0148v1

Mathematics

Symplectic Geometry

Scientific paper

n this paper we define an invariant of a pair of 6 dimensional symplectic %optional manifold with vanishing 1st Chern class and its Lagrangian submanifold with vanishing Maslov index. This invariant is a function on the set of the path connected components of the bounding cochains (solution of A infinity version of Maurer-Cartan equation of the filtered A infinity algebra associated to the Lagrangian submanifold). In the case when the Lagrangian submanifold is a rational homology sphere, it becomes a numerical invariant. This invariant depends on the choice of almost complex structure. The way how it depends on the almost complex structure is described by a wall crossing formula which involves moduli space of pseudo-holomorphic spheres.

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