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An elementary section of a bundle


Author: A. Rigas
Journal: Proc. Amer. Math. Soc. 102 (1988), 1099-1100
MSC: Primary 55R10; Secondary 17A35, 55Q52
DOI: https://doi.org/10.1090/S0002-9939-1988-0934896-6
MathSciNet review: 934896
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Abstract: We use the Cayley algebra and triality to provide an explicit section of a principal $ {G_2}$-bundleover $ {S^7}$. This section is the basic ingredient for a direct, elementary, proof that $ {\pi _6}{G_2} \cong {{\mathbf{Z}}_3},{\pi _6}SU(3) \cong {{\mathbf{Z}}_6}$ and $ {\pi _6}{S^3} \cong {{\mathbf{Z}}_{12}}$


References [Enhancements On Off] (What's this?)

  • [C] É. Cartan, Le principe de dualité et la théorie des groupes simples et semi-simples, Bull. Sci. Math. 49 (1925), 361-374.
  • [H-L] R. Harvey and B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47-157. MR 666108 (85i:53058)
  • [M] M. Mimura, The homotopy groups of Lie groups of low rank, J. Math. Kyoto Univ. 6-2 (1967), 131-176. MR 0206958 (34:6774)
  • [P] I. R. Porteous, Topological geometry, 2nd ed., Cambridge Univ. Press, 1981. MR 606198 (82c:51018)
  • [W] G. Whitehead, Elements of homotopy theory. I, Springer-Verlag, 1978. MR 516508 (80b:55001)
  • [S] J.-P. Serre, Groupes d'homotopie e classes de groupes Abéliens, Ann. of Math. 58 (1953), 258-294. MR 0059548 (15:548c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934896-6
Article copyright: © Copyright 1988 American Mathematical Society

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