A Property of Lie Group Orbits
Printed: Mar 2000
Let $G$ be a real Lie group and $X$ a real analytic manifold.
Suppose that $G$ acts analytically on $X$ with finitely many
orbits. Then the orbits are subanalytic in $X$. As a consequence
we show that the micro-support of a $G$-equivariant sheaf on $X$ is
contained in the conormal variety of the $G$-action.
32B20 - Semi-analytic sets and subanalytic sets [See also 14P15]
22E15 - General properties and structure of real Lie groups