The stratified spaces of a symplectic Lie group action

In this paper we show that the classical symplectic stratification theorem of the reduced spaces of a canonical group action in a symplectic manifold can be obtained even in the absence of a momentum map by replacing this object by its natural generalization, the cylinder valued momentum map introduced by Condevaux, Dazord, and Molino. In the process of proving this result we will provide a normal form for the cylinder valued momentum map.