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Pseudoholomorphic Strips in Symplectisations II: Fredholm Theory and Transversality

Summary: Pseudoholomorphic Strips in Symplectisations II:
Fredholm Theory and Transversality
Michigan State University
This paper is part of a larger program, the investigation of the chord problem in
three dimensional contact geometry. The main tool will be pseudoholomorphic
strips in the symplectisation of a three dimensional contact manifold with two
totally real submanifolds L0, L1 as boundary conditions. The submanifolds L0
and L1 do not intersect transversally. In this paper we will develop a nonlinear
Fredholm theory that guarantees the existence of a family of embedded pseudo-
holomorphic strips near a given one with suitable properties. c 2003 Wiley
Periodicals, Inc.
1. Introduction 1
2. Some Properties of the Solutions 9
3. Setting up the Nonlinear Equation in the Normal Direction 11
4. The Linearized Problem: Fredholm theory and Transversality 34
Appendix A. The Similarity Principle 55
Appendix B. Uniformization of (S, i(z)) 57


Source: Abbas, Casim - Department of Mathematics, Michigan State University


Collections: Mathematics