Franklin

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

Author/Creator:
Wendl, Chris, author.
Publication:
Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.
Series:
Cambridge tracts in mathematics ; 220.
Cambridge tracts in mathematics ; 220
Format/Description:
Book
viii, 185 pages : illustrations ; 24 cm.
Subjects:
Symplectic and contact topology.
Pseudoholomorphic curves.
Contact manifolds.
Manifolds (Mathematics).
Holomorphic functions.
Intersection theory (Mathematics).
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
9781108759588
OCLC:
1119618718
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