Stratified Subcartesian Spaces

http://dx.doi.org/10.4153/CMB-2011-026-3
Canad. Math. Bull. 54(2011), 693-705

  Published:2011-03-05
 Printed: Dec 2011

We show that if the family $\mathcal{O}$ of orbits of all vector fields on a subcartesian space $P$ is locally finite and each orbit in $\mathcal{O}$ is locally closed, then $\mathcal{O}$ defines a smooth Whitney A stratification of $P$. We also show that the stratification by orbit type of the space of orbits $M/G$ of a proper action of a Lie group $G$ on a smooth manifold $M$ is given by orbits of the family of all vector fields on $M/G$.