Holomorphic Curves in Low Dimensions From Symplectic Ruled Surfaces to Planar Contact Manifolds /

• Main Author: Wendl, Chris (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes in Mathematics, 2216
• Subjects: Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Global analysis (Mathematics).; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).; Global Analysis and Analysis on Manifolds.

This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of th...

Table of Contents:

• 1 Introduction
• 2 Background on Closed Pseudoholomorphic Curves
• 3 Blowups and Lefschetz Fibrations
• 4 Compactness
• 5 Exceptional Spheres
• 6 Rational and Ruled Surfaces
• 7 Uniruled Symplectic 4-Manifolds
• 8 Holomorphic Curves in Symplectic Cobordisms
• 9 Contact 3-Manifolds and Symplectic Fillings
• Appendix
• Bibliography
• Index.