IAS /Park City Mathematics S eries
Volume 7 , 1999Introduction to Symplectic Topology
Dusa McDuff
Introduction
Instead of t rying to give a comprehensive overview of the subject, I will con-
centrate on explaining a few key concepts and their implications, notably "Moser 's
argument" (or the homotopy method) in Lecture 2, capacity in Lecture 4 and
Gromov's proof of the nonsqueezing theorem in Lecture 5. The first exhibits the
flexibility of symplectic geometry while the latter two show its rigidity. Quite a lot
of time is spent on the linear theory since t his is the basis of everything else. The
last lecture sketches the bare outlines of t he theory of J-holomorphic spheres, to
give an introduction to a fascinating and powerful technique.
Throughout the notation is consistent with t hat used in [MSl] and [MS2].
Readers may consult those books for more details on almost every topic mentioned
here, as well as for a much fuller list of references.
I wish to thank J enn Slimowitz for taking the notes and making useful com-
ments on an earlier version of this manuscript.
(^1) Math. Dept., SUNY, Stony Brook, NY 11794.
E-mail address: dus a©math. sunysb. edu.
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@ 1999 American Mathematical Society