An Introduction to Compactness Results in Symplectic Field Theory

1. Front Matter

   Pages I-VIII

   PDF

2. Riemann Surfaces

   • Casim Abbas

   Pages 1-99

3. Pseudoholomorphic Curves

   • Casim Abbas

   Pages 101-207

4. The SFT Compactness Results

   • Casim Abbas

   Pages 209-245

5. Back Matter

   Pages 247-252

   PDF

This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.

• Contact homology
• Contact topology
• Symplectic field theory
• Symplectic manifolds
• Symplectic structures of moduli spaces

From the book reviews:

“A unified and detailed presentation of the symplectic field theory (SFT) is given with desire to make it more accessible. Proofs of the compactness results in SFT are presented with considerably more details and background material. … The book is of interest both for non-specialists and specialists in SFT, and also for graduate students.” (Gheorghe Zet, zbMATH, Vol. 1288, 2014)

• Department of Mathematics, Michigan State University, East Lansing, USA

  Casim Abbas

Policies and ethics