Exponential Decay Estimates and Smoothness of the Moduli Space of Pseudoholomorphic Curves

Kenji Fukaya, State University of New York, Stony Brook, New York, Yong-Geun Oh, Institute for Basic Sciences, Pohang, Korea, and POSTECH, Pohang, Korea, Hiroshi Ohta, Nagoya University, Japan, and Kaoru Ono, Kyoto University, Japan.

1. Introduction 2. Preliminaries 3. Statement of the gluing theorem 4. Proof of the gluing theorem I: Cut-off functions and weighted Sobolev norm 5. Proof of the gluing theorem II: Gluing by alternating method 6. Exponential decay of $T$ derivatives 7. Surjectivity and injectivity of the gluing map 8. Exponential decay estimate implies smoothness of coordinate change A. Error term estimate of non-linear Cauchy-Riemann equation I B. Estimate of Parallel transport 1 C. Error term estimate of non-linear Cauchy-Riemann equation II D. Estimate of Parallel transport 2 E. Estimate of the non-linearity of Exponential map F. Estimate of Parallel transport 3 G. Estimate of $T$ derivative of the error term of non-linear Cauchy-Riemann equation H. Proof of Lemma