MATH 7570: Topics in Topology (fall 2008)

Instructor: Tomoo Matsumura

The goal of this course is to provide a fast introduction to Poisson geometry, following Izu Vaisman's Lectures on the geometry of Poisson manifolds. We will learn about Poisson manifolds, Schouten-Nijenhuis bracket, symplectic foliations, Poisson calculus and Poisson (co)homology, symplectic realization of Poisson manifolds and symplectic groupoids. Some recent topics may be covered toward the end, depending on students' interests. Students are expected to know the basics of differentiable manifolds and have knowledge of de Rham cohomology, such as is covered in MATH 652. Comfort with algebraic topology may be helpful.