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arXiv · 0908.0148

Counting pseudo-holomorphic discs in Calabi-Yau 3 fold

Kenji Fukaya
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Abstract

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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Kenji Fukaya. 2009-08-02. Counting pseudo-holomorphic discs in Calabi-Yau 3 fold. https://arxiv.org/abs/0908.0148

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