2009/08/02 by Kenji Fukaya, Fukaya, Kenji · 1 citation
Mathematics · #53D12 #53D40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0908.0148
openalex publication_date 2009/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.