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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stable orbits of differentiable group actions


Author: Dennis Stowe
Journal: Trans. Amer. Math. Soc. 277 (1983), 665-684
MSC: Primary 57S20; Secondary 57R30, 58F18
MathSciNet review: 694382
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694382-8
PII: S 0002-9947(1983)0694382-8
Article copyright: © Copyright 1983 American Mathematical Society