Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction: Motivation
- Lecture 1 Closed Holomorphic Curves in Symplectic 4-Manifolds
- Lecture 2 Intersections, Ruled Surfaces, and Contact Boundaries
- Lecture 3 Asymptotics of Punctured Holomorphic Curves
- Lecture 4 Intersection Theory for Punctured Holomorphic Curves
- Lecture 5 Symplectic Fillings of Planar Contact 3-Manifolds
- Appendix A Properties of Pseudoholomorphic Curves
- Appendix B Local Positivity of Intersections
- Appendix C A Quick Survey of Siefring’s Intersection Theory
- References
- Index
Introduction: Motivation
Published online by Cambridge University Press: 06 March 2020
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Introduction: Motivation
- Lecture 1 Closed Holomorphic Curves in Symplectic 4-Manifolds
- Lecture 2 Intersections, Ruled Surfaces, and Contact Boundaries
- Lecture 3 Asymptotics of Punctured Holomorphic Curves
- Lecture 4 Intersection Theory for Punctured Holomorphic Curves
- Lecture 5 Symplectic Fillings of Planar Contact 3-Manifolds
- Appendix A Properties of Pseudoholomorphic Curves
- Appendix B Local Positivity of Intersections
- Appendix C A Quick Survey of Siefring’s Intersection Theory
- References
- Index
Summary
The introduction motivates the remainder of the book via two specific examples of theorems from the early days of symplectic topology in which intersection theory plays a prominent role. We sketch closely analogous proofs of both theorems, emphasizing the way that intersection theory is used, but point out why the second theorem (on symplectic 4-manifolds that are standard near infinity) requires a nonobvious extension of homological intersection theory to punctured holomorphic curves. We then discuss informally some of the properties this theory will need to have and what kinds of subtle issues may arise.
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- Publisher: Cambridge University PressPrint publication year: 2020