Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory

Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.

• Presents an accessible introduction to the intersection theory of punctured holomorphic curves and its applications
• Features self-contained proofs of the similarity principle and positivity of intersections, some of which have not appeared elsewhere in the literature
• Includes a 'quick reference' appendix summarizing the main results needed to use the intersection theory in applications