Counting pseudo-holomorphic discs in Calabi-Yau 3-holds

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概要

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• In this paper we define an invariant of a pair of a 6 dimensional symplectic manifold with vanishing 1st Chern class and its relatively spin Lagrangian submanifold with vanishing Maslov index. This invariant is a function on the set of the path connected components of bounding cochains (solutions of the $A_{\infty}$ version of the Maurer-Cartan equation of the filtered $A_{\infty}$ 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 structures. The way how it depends on the almost complex structures is described by a wall crossing formula which involves a moduli space of pseudo-holomorphic spheres.

著者

• Fukaya Kenji

  Department Of Mathematics Kyoto University

関連論文

• Counting pseudo-holomorphic discs in Calabi-Yau 3-holds
• Collapsing Riemannian manifolds to ones with lower dimension II

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