Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Homotopy periodicity and coherence

Authors: Ross Geoghegan and Andrew Nicas
Journal: Proc. Amer. Math. Soc. 124 (1996), 2889-2895
MSC (1991): Primary 55P10; Secondary 57S05, 55M35, 20F34
MathSciNet review: 1346975
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [Br] K. S. Brown, Cohomology of Groups, Springer--Verlag, New York, 1982. MR 83k:20002
  • [BG] K. S. Brown and R. Geoghegan, An infinite dimensional torsion-free $FP_{\infty }$ group, Invent. Math. 77 (1984), 367--381. MR 85m:20073
  • [C] G. Cooke, Replacing homotopy actions by topological actions, Trans. Amer. Math. Soc. 237 (1978), 391--406. MR 57:1529
  • [D] J. Dugundji, Topology, Allyn & Bacon, Boston, 1965. MR 33:1824
  • [F] S. Ferry, Homotopy, simple homotopy and compacta, Topology 19 (1980), 101--110. MR 81j:57010
  • [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

Similar Articles

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

Retrieve articles in all journals with MSC (1991): 55P10, 57S05, 55M35, 20F34

Additional Information

Ross Geoghegan
Affiliation: Department of Mathematics, State University of New York at Binghamton, Binghamton, New York 13902–6000

Andrew Nicas
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

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
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society