Homotopy periodicity and coherence
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- by Ross Geoghegan and Andrew Nicas
- Proc. Amer. Math. Soc. 124 (1996), 2889-2895
- DOI: https://doi.org/10.1090/S0002-9939-96-03543-5
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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.References
- Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR 672956, DOI 10.1007/978-1-4684-9327-6
- Kenneth S. Brown and Ross Geoghegan, An infinite-dimensional torsion-free $\textrm {FP}_{\infty }$ group, Invent. Math. 77 (1984), no. 2, 367–381. MR 752825, DOI 10.1007/BF01388451
- George Cooke, Replacing homotopy actions by topological actions, Trans. Amer. Math. Soc. 237 (1978), 391–406. MR 461544, DOI 10.1090/S0002-9947-1978-0461544-2
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, MA, 1966. MR 193606
- Steve Ferry, Homotopy, simple homotopy and compacta, Topology 19 (1980), no. 2, 101–110. MR 572578, DOI 10.1016/0040-9383(80)90001-4
- R. Geoghegan and A. Nicas, Higher Euler characteristics, I, L’Enseign. Math. 41 (1995), 3–62.
- Harold M. Hastings and Alex Heller, Homotopy idempotents on finite-dimensional complexes split, Proc. Amer. Math. Soc. 85 (1982), no. 4, 619–622. MR 660617, DOI 10.1090/S0002-9939-1982-0660617-5
Bibliographic Information
- 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
- MR Author ID: 131000
- Email: nicas@mcmaster.ca
- 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 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2889-2895
- MSC (1991): Primary 55P10; Secondary 57S05, 55M35, 20F34
- DOI: https://doi.org/10.1090/S0002-9939-96-03543-5
- MathSciNet review: 1346975