On the existence and classification of extensions of actions on submanifolds of disks and spheres

Assadi, Amir; Browder, William

doi:10.1090/S0002-9947-1985-0800249-6

On the existence and classification of extensions of actions on submanifolds of disks and spheres
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by Amir Assadi and William Browder

Trans. Amer. Math. Soc. 291 (1985), 487-502

DOI: https://doi.org/10.1090/S0002-9947-1985-0800249-6

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Abstract:

Given a $G$-action $\psi :G \times W \to W$ and an embedding $W \subset {D^n}$, when is it possible to find a $G$-action $\phi :G \times {D^n} \to D$ such that ${D^n} - W$ is $G$-free? Sufficient conditions of cohomological nature for the existence of such extensions are given and the extensions are classified. This leads to the characterization of the stationary point sets and classification of semifree actions on disks up to $G$-diffeomorphism under suitable dimension hypotheses.

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