In 1991, Sjamaar and Lerman [1] introduced the notion of stratified symplectic spaces. Namely, if $M$ is a symplectic manifold and $G$ a Lie group acting properly (but not necessarily freely) on $M$ and there is a moment map $\mu:M\to{\frak g}^*$ for this action, then they show that the symplectic reduction $$M//G:=\mu^{-1}(0)/G$$ is union a symplectic manifolds that "fit nicely together", in the sense that they form a topological stratification of $M$.
In another 1991 paper [2], which summarizes the results of [1], Sjamaar and Cushman pose the following problem:
"Try to generalize the results of this paper to any of the various infinite-dimensional situations arising in mathematical physics, e.g. Yang-Mills theory and the Einstein equations."
Has there been some progress towards this goal?
[1] Reyer Sjamaar and Eugene Lerman, MR 1127479 Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375--422.
[2] Richard Cushman and Reyer Sjamaar, On singular reduction of Hamiltonian spaces, Progr. Math. 99 (1991), 114-128.
