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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[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), 478-483. MR**22**#5959. MR**0115157 (22:5959)****[3]**T. A. Chapman,*Cell-like mappings of Hilbert cube manifolds: Applications to simple homotopy theory*(preprint). MR**0326740 (48:5083)****[4]**-,*Cell-like 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), 52-56. MR**49**#11518. MR**0346794 (49:11518)****[6]**M. M. Cohen,*A course in simple-homotopy theory*, Springer-Verlag, 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 cell-like 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, 52-68. 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, A-809. Abstract #699-G22.**[11]**J. E. West,*Mapping cylinders of Hilbert cube factors*, General Topology and Appl.**1**(1971), no. 2, 111-125. MR**44**#5984. MR**0288788 (44:5984)****[12]**R. Y. T. Wong,*Periodic actions on the Hilbert cube*(preprint). MR**0358844 (50:11303)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
57E25,
57A20

Retrieve articles in all journals with MSC: 57E25, 57A20

Additional Information

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

Keywords:
Hilbert cube manifolds,
semifree periodic homeomorphisms,
fixed point set,
simple homotopy equivalence,
CW-complex

Article copyright:
© Copyright 1977
American Mathematical Society