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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The stationary set of a group action


Author: Dennis Stowe
Journal: Proc. Amer. Math. Soc. 79 (1980), 139-146
MSC: Primary 57S20
MathSciNet review: 560600
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Abstract: If a point is stationary for a differentiable group action, M. Hirsch suggested that the vanishing of the first group cohomology at that point might imply stability of the point under perturbations of the action. This is proved for compactly generated Lie groups. Further implications of the cohomology condition are also proved.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0560600-2
PII: S 0002-9939(1980)0560600-2
Keywords: Topological group, group action, stability, semisimple Lie group, group cohomology
Article copyright: © Copyright 1980 American Mathematical Society