Symplectic

Proper maps in various categories studied in singularity theory (for example, the real analytic category) are known to be constructible, in the sense that the image of the map can be stratified in such a way that the map is a topologically locally trivial fibration over each stratum. In this talk we will present an equivariant analogue of this fact for momentum maps of Hamiltonian actions by compact Lie groups. This provides insight into when the symplectic reduced spaces change as we vary the value at which we perform reduction. After discussing this, we will explain a stratum-wise version of the Duistermaat-Heckman linear variation theorem and, time permitting, we will touch upon an instance of an invariant cycle type theorem for momentum maps.