Stratified Subcartesian Spaces

Details Stratified Subcartesian Spaces Stratified Subcartesian Spaces

2008-05-30

arxiv.org/abs/0805.4807v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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

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