Orbits of Lie Group Actions are Weakly Embedded

Details Orbits of Lie Group Actions are Weakly Embedded Orbits of Lie Group Actions are Weakly Embedded

2000-11-28

arxiv.org/abs/math/0011241v1

Mathematics

Differential Geometry

5 pages

Scientific paper

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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