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 4 - Intersection Theory for Punctured Holomorphic Curves
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
Using the relative asymptotic results of the previous lecture as a black box, this lecture explains the main definitions and results of Siefring’s intersection theory for punctured holomorphic curves. This includes the definition of a homotopy-invariant algebraic intersection number (the so-called “star-pairing”), the notion of hidden intersections at infinity and asymptotic positivity of intersections, and a punctured generalization of the adjunction formula.
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- Publisher: Cambridge University PressPrint publication year: 2020