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Homotopy Groups of Compact Lie Groups E6, E7 and E8

Published online by Cambridge University Press:  22 January 2016

Hideyuki Kachi
Hideyuki Kachi*
Affiliation:
Mathematical Institute, Nagoya University
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Let G be a simple, connected, compact and simply-connected Lie group. If k is the field with characteristic zero, then the algebra of cohomology H*(G ; k) is the exterior algebra generated by the elements x 1, …, xl of the odd dimension n1 , …, nl ; the integer l is the rank of G and is the dimension of G.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 109 - 139
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Adams, J. F.: On the group J(X) IV, Topology, 5–1 (1966), 21–71.Google Scholar
[2] Araki, S.: Cohomology modulo 2 of the compact exceptional groups E6 and E7 , J. of Math. Osaka C.V., Vol. 12 (1961), 43–65.Google Scholar
[3] Araki, S. and Shikata, Y.: Cohomology mod 2 of the compact exceptional group E8 , Proc. Japan Acad., 37 (1961), 619–622.Google Scholar
[4] Blakers, A.L. and Massey, W.S.: The homotopy groups of a triad II, Ann. of Math., 55 (1952), 192–201.Google Scholar
[5] Bott, R.: The stable homotopy of the classical groups, Ann. of Math., 70 (1959), 313–337.Google Scholar
[6] Bott, R. and Samelson, H.: Application of the theory of Morse to symmetric spaces, Amer. J. Math., 80 (1958), 964-1029.Google Scholar
[7] Cartan, H. and Serre, J.P.: Espaces fibrés et groupes d’homotopie I, II, C.R. Acad. Sci. Paris., 234 (1952), 288–290, 393–395.Google Scholar
[8] Serre, J.P.: Groupes d’homotopie et classes de groupes abélian, Ann. of Math., 58 (1953), 258–294.Google Scholar
[9] Serre, J.P.: Cohomologie modulo 2 des complexes d’Eilenberg Mac-Lane, Comm. Math. Helv., 27 (1953), 198–231.Google Scholar
[10] Mimura, M.: The homotopy group of Lie groups of low rank, J. Math. Kyoto Univ., 6–2 (1967), 131–176.Google Scholar
[11] Toda, H.: Composition methods in homotopy groups of spheres, Ann. of Math. Studies., (1962).Google Scholar