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Applications of group actions on finite complexes to Hilbert cube manifolds

Author: Leon Stagg Newman
Journal: Proc. Amer. Math. Soc. 62 (1977), 183-187
MSC: Primary 57E25; Secondary 57A20
MathSciNet review: 0431236
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Abstract: For any compact Hilbert cube manifold M such that $ {\tilde H_\ast}(M,{Z_p})$, there exists an embedding g of M into the Hilbert cube Q such that $ g(M)$ is the fixed point set of a semifree periodic homeomorphism of Q with period p. A counterexample is given to the conjecture that any two proper homotopic period p homeomorphisms of a Hilbert cube manifold such that the homeomorphisms revolve trivially about a unique fixed point are equivalent. A counterexample is also given for the case where the fixed point set is empty.

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Keywords: Hilbert cube manifolds, semifree periodic homeomorphisms, fixed point set, simple homotopy equivalence, CW-complex
Article copyright: © Copyright 1977 American Mathematical Society

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