Stratifications of inertia spaces of compact Lie group actions
  We study the topology of the inertia space of a smooth $G$-manifold $M$ where $G$ is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demonstrating that the inertia space is a triangulable differentiable stratified space. In addition, we demonstrate a de Rham theorem for differential forms defined on the inertia space with respect to this stratification. 
Carla Farsi, Markus J. Pflaum, Christopher Seaton
math.DG math.AT