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

DOI:
https://doi.org/10.1090/S0002-9939-1977-0431236-9

MathSciNet review:
0431236

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Abstract | References | Similar Articles | Additional Information

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