University of Toronto's Symplectic Geometry Seminar

Thursday May 19, 2005
SS 5017A

Rui Fernandes


Linearization of Poisson brackets

Abstract: If one fixes a symplectic leaf of a Poisson manifold, there is a linear model for the Poisson bracket in a neighborhood of the leaf. The linearization problem is to decide if there is a Poisson diffeomorphism from a tubular neighborhood of the leaf to this linear model. An old result of J. Conn states that Poisson brackets can be linearized around fixed points (i.e., zero dimensional leafs) with compact semisimple linear part. I will give a new geometric proof of Conn's result, using Moser's path method, and formulate a conjecture for higher dimensional leafs.