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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On odd-primary components of Lie groups

Author: K. Knapp
Journal: Proc. Amer. Math. Soc. 79 (1980), 147-152
MSC: Primary 55Q45; Secondary 57R90
MathSciNet review: 560601
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Abstract: The transfer map $ t:{\pi ^s}({P_\infty }{\mathbf{C}}) \to {\pi ^s}({S^0})$ is represented by an element $ \tau \in \pi _s^{ - 1}({P_\infty }{{\mathbf{C}}^ + })$. We compute the Adams-e-invariant of $ \tau $ and use this and the splitting of the p-localization of $ {S^1} \wedge {P_\infty }{\mathbf{C}}$ into a wedge of $ (p - 1)$ spaces to prove that for a prime $ p \geqslant 5$ the p-component of the element $ [G,\mathcal{L}]$ defined by a compact Lie group G in $ \pi _ \ast ^s$ is zero in the known part of stable homotopy.

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

  • [1] J. F. Adams, On the groups 𝐽(𝑋). II, Topology 3 (1965), 137–171. MR 0198468 (33 #6626)
  • [2] J. M. Boardman, Stable homotopy theory, duality and Thom spectra (mimeographed notes), Chapter 5, University of Warwick, 1966.
  • [3] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. II, Amer. J. Math. 81 (1959), 315–382. MR 0110105 (22 #988)
  • [4] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968 (French). MR 0240238 (39 #1590)
  • [5] K. Knapp, Rank and Adams filtration of a Lie group, Topology 17 (1978), no. 1, 41–52. MR 0470960 (57 #10703)
  • [6] H. R. Miller, Some algebraic aspects of the Adams-Novikov spectral sequence, Dissertation, Princeton Univ., Princeton, N. J., 1974.
  • [7] Mamoru Mimura, Goro Nishida, and Hirosi Toda, 𝑀𝑜𝑑\𝑝 decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977/78), no. 3, 627–680. MR 0478187 (57 #17675)
  • [8] Shichirô Oka, The stable homotopy groups of spheres. III, Hiroshima Math. J. 5 (1975), no. 3, 407–438. MR 0394651 (52 #15452)
  • [9] V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. Prentice-Hall Series in Modern Analysis. MR 0376938 (51 #13113)

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Additional Information

PII: S 0002-9939(1980)0560601-4
Keywords: Transfer, stable homotopy, Lie groups, e-invariant, filtration in the Adams spectral sequence
Article copyright: © Copyright 1980 American Mathematical Society

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