The mod C Suspension Theorem
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 684-701

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Our aim in this paper is to prove the general mod C suspension theorem: Suppose that X and Y are CW-complexes,C is a class offinite abelian groups, and that(i) πi(Y) ∈Cfor all i < n,(ii) H*(X; Z) is finitely generated,(iii) Hi(X;Z) ∈Cfor all i > k. Then the suspension homomorphism is a(mod C) monomorphism for 2 ≦ r ≦ 2n – k – 2 (when r= 1, ker E is a finite group of order d, where Zd ∈ C and is a (mod C) epimorphism for 2 ≦ r ≦ 2n – k – 2The proof is basically the same as the proof of the regular suspension theorem. It depends essentially on (mod C) versions of the Serre exact sequence and of the Whitehead theorem.
Brown, Benson Samuel. The mod C Suspension Theorem. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 684-701. doi: 10.4153/CJM-1969-078-7
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[1] 1. Barcus, W. D. and Meyer, J.-P., The suspension of a loop space, Amer. J. Math. 80 (1958), 895–920. Google Scholar

[2] 2. Cartan, H., Algèbres a“Eilenberg-MacLane et homotopie, Séminaire Henri Cartan, 1954-1955 (Secrétariat mathématique, Paris, 1956). Google Scholar

[3] 3. Eckmann, B. and Hilton, P. J., Décomposition homologique d'un polyèdre simplement connexe, C. R. Acad. Sci. Paris 248 (1959), 2054–2056. Google Scholar

[4] 4. Eilenberg, S. and MacLane, S., Relations between homology and homotopy groups of spacest Ann. of Math. (2) 46 (1945), 480–509 Google Scholar

[5] 5. Hu, S.-T., Homotopy theory, Pure and Applied Mathematics , Vol. VIII (Academic Press, New York, 1959). Google Scholar

[6] 6. Moore, J. C., On homotopy groups of spaces with a single non-vanishing homology group, Ann. of Math. (2) 59 (1954), 549–557. Google Scholar

[7] 7. Serre, J.-P., Homologie singulière des espaces fibres. Applications, Ann. of Math. (2) 54 (1951), 425–505. Google Scholar

[8] 8. Serre, J.-P., Groupes d'homotopie et classes de groupes abêliens, Ann. of Math. (2) 58 (1953), 258–294. Google Scholar

[9] 9. Serre, J.-P., Cohomologie modulo 2 des complexes à“Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198–232. Google Scholar

[10] 10. Spanier, E. H., Duality and the suspension category, International Symposium on Algebraic Topology, Symposium Internacional de Topologia Algebrica, 1956 (Universidad Nacional Atonoma de Mexico, UNESCO, 1958). Google Scholar

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