Applications of group actions on finite complexes to Hilbert cube manifolds
Author:
Leon Stagg Newman
Journal:
Proc. Amer. Math. Soc. 62 (1977), 183187
MSC:
Primary 57E25; Secondary 57A20
MathSciNet review:
0431236
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Abstract: For any compact Hilbert cube manifold M such that , there exists an embedding g of M into the Hilbert cube Q such that 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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M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478483. MR 22 #5959. MR 0115157 (22:5959)
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T. A. Chapman, Celllike mappings of Hilbert cube manifolds: Applications to simple homotopy theory (preprint). MR 0326740 (48:5083)
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, Celllike mappings of Hilbert cube manifolds: Solution of a handle body problem (preprint).
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, Compact Hilbert cube manifolds and the invariance of Whitehead torsion, Bull. Amer. Math. Soc. 79 (1973), 5256. MR 49 #11518. MR 0346794 (49:11518)
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M. M. Cohen, A course in simplehomotopy theory, SpringerVerlag, New York, 1973. MR 50 #14762 MR 0362320 (50:14762)
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D. A. Edwards, H. M. Hastings and J. West, Group actions on infinite dimensional manifolds (preprint).
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A. Fathi, A celllike map between Hilbert cube manifolds is a near homeomorphism, a short proof (preprint).
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L. E. Jones, The converse to the fixed point theorem of P. A. Smith. I, Ann. of Math. (2) 94 (1971), no. 1, 5268. MR 45 #4427. MR 0295361 (45:4427)
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R. M. Schori and D. W. Curtis, Hyperspaces of compact connected polyhedra, Notices Amer. Math. Soc. 19 (1972), no. 141, A809. Abstract #699G22.
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J. E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no. 2, 111125. MR 44 #5984. MR 0288788 (44:5984)
 [12]
R. Y. T. Wong, Periodic actions on the Hilbert cube (preprint). MR 0358844 (50:11303)
 [1]
 R. D. Anderson and Nelly Kroonenberg, Open problems in infinite dimensional topology (preprint). MR 0358788 (50:11247)
 [2]
 M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478483. MR 22 #5959. MR 0115157 (22:5959)
 [3]
 T. A. Chapman, Celllike mappings of Hilbert cube manifolds: Applications to simple homotopy theory (preprint). MR 0326740 (48:5083)
 [4]
 , Celllike mappings of Hilbert cube manifolds: Solution of a handle body problem (preprint).
 [5]
 , Compact Hilbert cube manifolds and the invariance of Whitehead torsion, Bull. Amer. Math. Soc. 79 (1973), 5256. MR 49 #11518. MR 0346794 (49:11518)
 [6]
 M. M. Cohen, A course in simplehomotopy theory, SpringerVerlag, New York, 1973. MR 50 #14762 MR 0362320 (50:14762)
 [7]
 D. A. Edwards, H. M. Hastings and J. West, Group actions on infinite dimensional manifolds (preprint).
 [8]
 A. Fathi, A celllike map between Hilbert cube manifolds is a near homeomorphism, a short proof (preprint).
 [9]
 L. E. Jones, The converse to the fixed point theorem of P. A. Smith. I, Ann. of Math. (2) 94 (1971), no. 1, 5268. MR 45 #4427. MR 0295361 (45:4427)
 [10]
 R. M. Schori and D. W. Curtis, Hyperspaces of compact connected polyhedra, Notices Amer. Math. Soc. 19 (1972), no. 141, A809. Abstract #699G22.
 [11]
 J. E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no. 2, 111125. MR 44 #5984. MR 0288788 (44:5984)
 [12]
 R. Y. T. Wong, Periodic actions on the Hilbert cube (preprint). MR 0358844 (50:11303)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197704312369
PII:
S 00029939(1977)04312369
Keywords:
Hilbert cube manifolds,
semifree periodic homeomorphisms,
fixed point set,
simple homotopy equivalence,
CWcomplex
Article copyright:
© Copyright 1977
American Mathematical Society
