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Transactions of the American Mathematical Society

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

 

 

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


Authors: Amir Assadi and William Browder
Journal: Trans. Amer. Math. Soc. 291 (1985), 487-502
MSC: Primary 57S17; Secondary 57R65, 57S25
DOI: https://doi.org/10.1090/S0002-9947-1985-0800249-6
MathSciNet review: 800249
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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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DOI: https://doi.org/10.1090/S0002-9947-1985-0800249-6
Article copyright: © Copyright 1985 American Mathematical Society