Cornell Math - MATH 758, Spring 2000

MATH 758 — Spring 2000
Topics in Symplectic Topology

A symplectic manifold is a smooth, even-dimensional manifold equipped with a smooth, non-degenerate, closed two-form. Such manifolds have played an important role in classical mechanics for well over a century, but only recently have they been studied extensively from a topological viewpoint. Many interesting examples of 4-manifolds are symplectic, as are Kaehler manifolds and (more generally) almost-complex manifolds. After some foundational material, this course will cover such topics as: constructing symplectic manifolds, pseudo-holomorphic curves, symplectic invariants, non-squeezing theorems, groups of symplectomorphisms, symplectic circle actions, and others. The course will make use of the book, "Introduction to Symplectic Topology," by MacDuff and Salamon, as well as papers by MacDuff, Gromov, and Gompf.

Prerequisites:

A course equivalent to Math 651 (algebraic topology) and a one-semester course in differential topology, or permission of the instructor.