Proceedings of the American Mathematical Society

Author(s): Ross Geoghegan; Andrew Nicas
Journal: Proc. Amer. Math. Soc. 124 (1996), 2889-2895.
MSC (1991): Primary 55P10; Secondary 57S05, 55M35, 20F34
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Abstract: If $f\colon \,Z \rightarrow Z$ is a periodic homotopy equivalence ( $\operatorname {id}_{Z} \simeq f^{p}$ ) or a homotopy idempotent ( $f \simeq f^{2}$ ), the question arises whether this periodicity property can be achieved by a homotopy ``compatible with'' $f$

. These coherence questions are answered.

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[C]: G. Cooke, Replacing homotopy actions by topological actions, Trans. Amer. Math. Soc. 237 (1978), 391--406. MR 57:1529
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[GN]: R. Geoghegan and A. Nicas, Higher Euler characteristics, I, L'Enseign. Math. 41 (1995), 3--62. CMP 95:15
[HH]: H. M. Hastings and A. Heller, Homotopy idempotents on finite dimensional complexes split, Proc. Amer. Math. Soc. 85 (1982), 619--622. MR 83j:55010

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55P10, 57S05, 55M35, 20F34

Ross Geoghegan
Affiliation: Department of Mathematics, State University of New York at Binghamton, Binghamton, New York 13902--6000
Email: ross@math.binghamton.edu

Andrew Nicas
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email: nicas@mcmaster.ca

DOI: 10.1090/S0002-9939-96-03543-5
PII: S 0002-9939(96)03543-5
Received by editor(s): February 6, 1995
Additional Notes: The first author was partially supported by the National Science Foundation.
The second author was partially supported by the Natural Sciences and Engineering Research Council of Canada.
Communicated by: James West
Copyright of article: Copyright 1996, American Mathematical Society

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