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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0560601-4
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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560601-4
Keywords: Transfer, stable homotopy, Lie groups, e-invariant, filtration in the Adams spectral sequence
Article copyright: © Copyright 1980 American Mathematical Society