Lectures on contact 3-manifolds, holomorphic curves and intersection theory / Chris Wendl.

Format:

Book

Author/Creator:

Wendl, Chris, author.

Series:

Cambridge tracts in mathematics ; 220.

Cambridge tracts in mathematics ; 220

Language:

English

Subjects (All):

Symplectic and contact topology.

Pseudoholomorphic curves.

Contact manifolds.

Manifolds (Mathematics).

Holomorphic functions.

Intersection theory (Mathematics).

Physical Description:

viii, 185 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.

Summary:

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.-- Publisher's description.

Contents:

Motivation

Closed holomorphic curves in symplectic 4-manifolds

Intersections, ruled surfaces, and contact boundaries

Asymptotics of punctured holomorphic curves

Intersection theory for punctured holomorphic curves

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.

Notes:

Includes bibliographical references (pages [177]-181) and index.

Other Format:

ebook version :

ISBN:

9781108497404

1108497403

OCLC:

1119618718