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On the structure of pseudo-holomorphic discs with totally real boundary conditions. (English) Zbl 0931.53023
We study the structure of \(J\)-holomorphic discs in relation to the Fredholm theory of pseudo-holomorphic discs with totally real boundary conditions in almost complex manifolds \((M,J)\). We prove that any \(J\)-holomorphic disc with totally real boundary condition that is injective in the interior except at a discrete set of points, which we call a “normalized disc”, must either have some boundary point that is regular and has multiplicity one, or satisfy that its image forms a smooth immersed compact surface (without boundary) with a finite number of self-intersections and a finite number of branch points.
In the course of proving this theorem, we also prove several theorems on the local structure of boundary points of \(J\)-holomorphic discs, and, as an application, we give the first complete treatment of the transversality result for Floer’s pseudo-holomorphic trajectories for Lagrangian intersections in symplectic geometry.
Reviewer: Y.-G.Oh (Madison)

MSC:
53C40 Global submanifolds
32Q65 Pseudoholomorphic curves
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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