Cornell Math - MATH 653, Spring 2006

MATH 653: Differentiable Manifolds II (Spring 2006)

Instructor: Reyer Sjamaar

Meeting Time & Room

Prerequisites: MATH 652. Some familiarity with Lie groups (e.g. MATH 650) will be helpful but not required.

We will explore Lie group actions on smooth manifolds. After establishing some basic results such as the slice theorem and the orbit type stratification, we will look in more detail at special classes of group actions, such as isometric, holomorphic and symplectic actions. We will concentrate on the symplectic case and examine the main properties of the moment map, such as the convexity and reduction theorems. If time allows we will study equivariant differential forms and prove the Atiyah-Bott-Berline-Vergne localization theorem.