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Triviality of simple fiber-preserving actions of tori on Hilbert-cube-fiber bundles


Author: Vo Thanh Liem
Journal: Proc. Amer. Math. Soc. 87 (1983), 549-554
MSC: Primary 57N20; Secondary 57S99
DOI: https://doi.org/10.1090/S0002-9939-1983-0684656-4
MathSciNet review: 684656
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Abstract: Let $ \sigma $ denote the standard based-free action of a torus $ T$ on the Hilbert cube $ Q$. It will be shown that every simple fiber-preserving action of $ T$ on $ Q \times B$, where $ B$ is a finite-dimensional, compact metric absolute retract, is fiber-preserving equivalent to the diagonal action $ \sigma \times {\text{i}}{{\text{d}}_B}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0684656-4
Keywords: Hurewicz fibration, fiber bundle, $ \alpha $-equivalence, semifree action, fiber-preserving map, reduced cone
Article copyright: © Copyright 1983 American Mathematical Society

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