Structural stability and group cohomology

Fleming, Philip J.

doi:10.1090/S0002-9947-1983-0682733-X

Structural stability and group cohomology
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by Philip J. Fleming

Trans. Amer. Math. Soc. 275 (1983), 791-809

DOI: https://doi.org/10.1090/S0002-9947-1983-0682733-X

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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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