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
Lecture 2 - Intersections, Ruled Surfaces, and Contact Boundaries
Published online by Cambridge University Press: 06 March 2020
- 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
This lecture concludes our survey of closed holomorphic curves with a discussion, in the first section, of local intersection numbers, positivity of intersections and the adjunction formula for closed holomorphic curves, and then, in the second section, with an explanation of how these figure into the proof of McDuff’s theorem on symplectic ruled surfaces. The last two sections then begin a shift in focus toward punctured holomorphic curves: this discussion starts with a general introduction to contact manifolds and their symplectic fillings and then continues by defining the moduli space of punctured asymptotically cylindrical holomorphic curves in a completed symplectic cobordism between contact manifolds.
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- Publisher: Cambridge University PressPrint publication year: 2020