Geodesic
Representation types and 2-primary homotopy groups of certain compact Lie groups
Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 297-324.

Voir la notice de l'article provenant de la source International Press of Boston

Bousfield has shown how the 2-primary $v_1$-periodic homotopy groups of certain compact Lie groups can be obtained from their representation ring with its decomposition into types and its exterior power operations. He has formulated a Technical Condition which must be satisfied in order that he can prove that his description is valid. We prove that a simply-connected compact simple Lie group satisfies his Technical Condition if and only if it is not $E_6$ or $Spin(4k+2)$ with $k$ not a 2-power. We then use his description to give an explicit determination of the 2-primary $v_1$-periodic homotopy groups of $E_7$ and $E_8$. This completes a program, suggested to the author by Mimura in 1989, of computing the $v_1$-periodic homotopy groups of all compact simple Lie groups at all primes.
DOI : 10.4310/HHA.2003.v5.n1.a13
Classification : 55Q52, 55T15, 57T20
Keywords: homotopy groups, exceptional Lie groups, representation theory 
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Donald M. Davis. Representation types and 2-primary homotopy groups of certain compact Lie groups. Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 297-324. doi : 10.4310/HHA.2003.v5.n1.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a13/

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