Math 581DA
Eric Babson
Eric Babson
Autumn 2004, Monday/Wednesday/Friday, 11:30
The course will follows McDuff and Salamon: Introduction to
Symplectic Topology.
The main topic will be the global study of symplectic manifolds. After some
brief motivation from physics, we will start with definitions of the
objects and maps to study: manifolds with symplectic, contact, complex and
Kahler structures and (Hamiltonian) symplectomorphisms. We will then look
at some of the basic constructions: moment maps, blow-ups, connected sums,
and quotients. In particular, we will give a localization theorem that
shows that in the compact case many invariants (e.g. equivariant DeRahm
cohomology) are detectable from the fixed points of a Hamiltonian circle
action.
Prerequisites: Math 544/5/6.