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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Structural stability and group cohomology


Author: Philip J. Fleming
Journal: Trans. Amer. Math. Soc. 275 (1983), 791-809
MSC: Primary 58F10; Secondary 58B99, 58D05, 58F09
DOI: https://doi.org/10.1090/S0002-9947-1983-0682733-X
MathSciNet review: 682733
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Abstract: We prove a version of the theorem of Stowe concerning the stability of stationary points of a differentiable group action which is valid on Hilbert manifolds. This result is then used to show that the vanishing of certain cohomology groups is sufficient to guarantee structural semistability for a differentiable action of a group of finite type on a closed smooth manifold. We then apply this to groups of diffeomorphisms of the circle.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0682733-X
Keywords: Group of finite type, group action, Hilbert manifold, stability of stationary points, structural stability, group cohomology
Article copyright: © Copyright 1983 American Mathematical Society