Stable orbits of differentiable group actions

Stowe, Dennis

doi:10.1090/S0002-9947-1983-0694382-8

Stable orbits of differentiable group actions
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Trans. Amer. Math. Soc. 277 (1983), 665-684 Request permission

Abstract:

We prove that a compact orbit of a smooth Lie group action is stable provided the first cohomology space vanishes for the normal representation at some (equivalently, every) point of the orbit. When the orbit is a single point, the acting group need only be compactly generated and locally compact for this conclusion to hold. Applied to foliations, this provides a sufficient condition for the stability of a compact leaf and includes the stability theorems of Reeb and Thurston and of Hirsch as cases.

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