Exact sequences in stable homotopy pair theory
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- by K. A. Hardie and A. V. Jansen PDF
- Trans. Amer. Math. Soc. 286 (1984), 803-816 Request permission
Abstract:
A cylinder-web diagram with associated diagonal sequences is described in stable homotopy pair theory. The diagram may be used to compute stable homotopy pair groups and also stable track groups of two-cell complexes. For the stable Hopf class $\eta$ the stable homotopy pair groups ${G_k}(\eta ,\eta )(k \leqslant 8)$ are computed together with some of the additive structure of the stable homotopy ring of the complex projective plane.References
-
B. Eckmann and P. J. Hilton, Groupes d’homotopie et dualité, C. R. Acad. Sci. Paris Sér. I Math. 246 (1958), 2444, 2555, 2991.
- K. A. Hardie, Bifunctors and the diagonal exact sequences of a cylinder-web diagram, Quaestiones Math. 3 (1978/79), no. 3, 167–179. MR 533529
- K. A. Hardie, On the category of homotopy pairs, Topology Appl. 14 (1982), no. 1, 59–69. MR 662812, DOI 10.1016/0166-8641(82)90047-5
- K. A. Hardie and A. V. Jansen, The Puppe and Nomura operators in the category of homotopy pairs, Categorical aspects of topology and analysis (Ottawa, Ont., 1980) Lecture Notes in Math., vol. 915, Springer, Berlin-New York, 1982, pp. 112–126. MR 659887
- K. A. Hardie and A. V. Jansen, Toda brackets and the category of homotopy pairs, Quaestiones Math. 6 (1983), no. 1-3, 107–128. MR 700243
- Mamoru Mimura, On the generalized Hopf homomorphism and the higher composition. I, J. Math. Kyoto Univ. 4 (1964), 171–190. MR 179793, DOI 10.1215/kjm/1250524712
- Masamitsu Mori, Homotopy groups of Stiefel manifolds, Mem. Fac. Sci. Kyushu Univ. Ser. A 27 (1973), 135–148. MR 319189, DOI 10.2206/kyushumfs.27.135
- Juno Mukai, Stable homotopy of some elementary complexes, Mem. Fac. Sci. Kyushu Univ. Ser. A 20 (1966), 266–282. MR 206953, DOI 10.2206/kyushumfs.20.266
- Juno Mukai, On the stable homotopy of a $Z_{2}$-Moore space, Osaka Math. J. 6 (1969), 63–91. MR 259910
- Dieter Puppe, Homotopiemengen und ihre induzierten Abbildungen. I, Math. Z. 69 (1958), 299–344 (German). MR 100265, DOI 10.1007/BF01187411
- Hirosi Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J., 1962. MR 0143217
- C. T. C. Wall, On the exactness of interlocking sequences, Enseign. Math. (2) 12 (1966), 95–100. MR 206943
- Noburu Yamamoto, Algebra of stable homotopy of Moore space, J. Math. Osaka City Univ. 14 (1963), 45–67. MR 157382
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 286 (1984), 803-816
- MSC: Primary 55Q10; Secondary 55Q05
- DOI: https://doi.org/10.1090/S0002-9947-1984-0760988-1
- MathSciNet review: 760988