Homotopy periodicity and coherence

Geoghegan, Ross; Nicas, Andrew

doi:10.1090/S0002-9939-96-03543-5

Homotopy periodicity and coherence
HTML articles powered by AMS MathViewer

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

PDF | Request permission

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