Some properties of $H$-spaces of rank $2$
HTML articles powered by AMS MathViewer
- by C. A. McGibbon PDF
- Proc. Amer. Math. Soc. 81 (1981), 121-124 Request permission
Abstract:
We study $H$-spaces with 3 cells. After one suspension the attaching map for the top cell is shown to have order at most 2. For such $H$-spaces localized away from 2, we obtain a new proof of a classification theorem due to Zabrodsky. We also show that under suitable restrictions in the 3 cell case, the vanishing of all Whitehead products implies the existence of a multiplication.References
- M. G. Barratt, I. M. James, and N. Stein, Whitehead products and projective spaces, J. Math. Mech. 9 (1960), 813–819. MR 0116331, DOI 10.1512/iumj.1960.9.59050
- A. L. Blakers and W. S. Massey, Products in homotopy theory, Ann. of Math. (2) 58 (1953), 295–324. MR 60820, DOI 10.2307/1969790
- I. M. James, Reduced product spaces, Ann. of Math. (2) 62 (1955), 170–197. MR 73181, DOI 10.2307/2007107
- I. M. James, On sphere-bundles over spheres, Comment. Math. Helv. 35 (1961), 126–135. MR 123332, DOI 10.1007/BF02567011
- Gerald J. Porter, Higher-order Whitehead products, Topology 3 (1965), 123–135. MR 174054, DOI 10.1016/0040-9383(65)90039-X
- G. J. Porter, Spaces with vanishing Whitehead products, Quart. J. Math. Oxford Ser. (2) 16 (1965), 77–84. MR 172292, DOI 10.1093/qmath/16.1.77
- Dieter Puppe, Some well known weak homotopy equivalences are genuine homotopy equivalences, Symposia Mathematica, Vol. V (INDAM, Rome, 1969/70) Academic Press, London, 1971, pp. 363–374. MR 0303528
- Dennis Sullivan, Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. Localization, periodicity, and Galois symmetry; Revised version. MR 0494074
- Hirosi Toda, Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J., 1962. MR 0143217
- A. Zabrodsky, On rank $2$ $\textrm {mod}$ odd $H$-spaces, New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972), London Math. Soc. Lecture Note Ser., No. 11, Cambridge Univ. Press, London, 1974, pp. 119–128. MR 0336742
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 121-124
- MSC: Primary 55P45; Secondary 55Q15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589152-9
- MathSciNet review: 589152