Homotopy nilpotency and associativity
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- by Arthur H. Copeland and Albert O. Shar PDF
- Proc. Amer. Math. Soc. 80 (1980), 487-490 Request permission
Abstract:
If $(Y,\mu )$ is an H-space then a measure of nonassociativity, called Homotopy Nuclear Nilpotency (HNN) is defined. We then calculate the HNN of thirteen H-spaces: the twelve classes of multiplications on ${S^3}$ and the one class on $S_{(2’)}^5$, the 5-sphere localized away from 2.References
- M. Arkowitz and C. R. Curjel, Some properties of the exotic multiplications on the three-sphere, Quart. J. Math. Oxford Ser. (2) 20 (1969), 171–176. MR 248816, DOI 10.1093/qmath/20.1.171
- I. Berstein and T. Ganea, Homotopical nilpotency, Illinois J. Math. 5 (1961), 99–130. MR 126277
- Richard Hubert Bruck, A survey of binary systems, Reihe: Gruppentheorie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0093552
- William J. Gilbert, Homotopical nilpotence of the seven sphere, Proc. Amer. Math. Soc. 32 (1972), 621–622. MR 288761, DOI 10.1090/S0002-9939-1972-0288761-9
- I. M. James, Multiplication on spheres. II, Trans. Amer. Math. Soc. 84 (1957), 545–558. MR 90812, DOI 10.1090/S0002-9947-1957-0090812-8
- I. M. James, On $H$-spaces and their homotopy groups, Quart. J. Math. Oxford Ser. (2) 11 (1960), 161–179. MR 133132, DOI 10.1093/qmath/11.1.161
- Mamoru Mimura and Hirosi Toda, The $(n+20)$-th homotopy groups of $n$-spheres, J. Math. Kyoto Univ. 3 (1963), 37–58. MR 157384, DOI 10.1215/kjm/1250524854
- C. W. Norman, Homotopy loops, Topology 2 (1963), 23–43. MR 146836, DOI 10.1016/0040-9383(63)90020-X
- Hirosi Toda, Note on cohomology ring of certain spaces, Proc. Amer. Math. Soc. 14 (1963), 89–95. MR 150763, DOI 10.1090/S0002-9939-1963-0150763-5
- Alexander Zabrodsky, Hopf spaces, North-Holland Mathematics Studies, Vol. 22, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976. MR 0440542
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 487-490
- MSC: Primary 55P45
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581011-X
- MathSciNet review: 581011