A Spectral Sequence for Cohomotopy
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 712-729

Voir la notice de l'article provenant de la source Cambridge University Press

For a prime number p let be the class of finite abelian groups whose orders are prime to p. For a finitely generated abelian group G, let Gp be the sum of the free and p-primary components of G. Our aim in this paper is to prove the following theorem.Theorem. Suppose that(i) Hi(X;Z) = 0 for i > k,(ii) for i > k – d Then there exists a spectral sequence with and the differential is given by
Brown, Benson Samuel. A Spectral Sequence for Cohomotopy. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 712-729. doi: 10.4153/CJM-1969-080-5
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[1] 1. Adams, J. F., Stable homotopy theory. Notes by Vasquez, A. T., University of California, Berkeley, 1961; lecture notes in mathematics, no. 3 (Springer-Verlag, Berlin, 1964). Google Scholar

[2] 2. Adem, J., The relations on Steenrod powers of cohomology classes, ﹛Algebraic geometry and topology), A symposium in honor of S. Lefschetz, pp. 191–238 (Princeton Univ. Press, Princeton, N.J., 1957). Google Scholar

[3] 3. Barcus, W. D. and Meyer, J.-P., The suspension of a loop space, Amer. J. Math. 80 (1958), 895–920. Google Scholar

[4] 4. Brown, B. S., The mod <E suspension theorem, Can. J. Math. 21 (1969), 684–701. Google Scholar

[5] 5. Brown, B. S., A first approximation to ﹛X, Y), Can. J. Math. 21 (1969), 702–711. Google Scholar

[6] 6. Cartan, H., Algebres d’ Eilenberg-MacLane et homotopie, Séminaire Henri Cartan, 1954-1955 (Secrétariat mathématique, 1956). Google Scholar

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

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

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

[10] 10. 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

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

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

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

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

[15] 15. Thomas, P. E., “A spectral sequence for X-theory”, Appendix m Lectures on K(X) by Bott, R. H., Harvard University, 1962. Google Scholar

[16] 16. Toda, H., p-primary components of homotopy groups. II. mod p Hopf invariant, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 31 (1958), 143–160. Google Scholar

[17] 17. Toda, H., p-primary components of homotopy groups. IV. Compositions and toric constructions, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 82 (1959), 297–332. Google Scholar

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