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Stratified Subcartesian Spaces

Published online by Cambridge University Press:  20 November 2018

Tsasa Lusala  and
Jędrzej Śniatycki
Tsasa Lusala
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, ABe-mail: [email protected]: [email protected]
Jędrzej Śniatycki
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, ABe-mail: [email protected]: [email protected]
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Abstract

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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 $M/G$.

Keywords

58A4057N80Subcartesian spacesorbits of vector fieldsstratificationsWhitney Conditions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 693 - 705
Copyright
Copyright © Canadian Mathematical Society 2011

References

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