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Orbits of Lie Group Actions are Weakly Embedded

Domenico P. L. Castrigiano·Sandra A. Hayes
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Abstract

In this note we prove that whenever a Lie group $G$ acts on a manifold $X$, then the orbit $Gx$ through any point $x$ of $X$ is a weakly embedded submanifold of $X$. The investigation of this problem was inspired by an application to Cat astrophe Theory.

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Domenico P. L. Castrigiano, Sandra A. Hayes. 2000-11-28. Orbits of Lie Group Actions are Weakly Embedded. https://arxiv.org/abs/math/0011241

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