Skip to main content Accessibility help

The mod 2 homology of the space of loops on the exceptional Lie group

  • Akira Kono (a1) and Kazumuto Kozima (a2)


The Hopf algebra structure of H*G, F2) and the action of the dual Steenrod algebra are completely and explicitly determined when G isone of the connected, simply connected, exceptional, simple Lie groups. The approach is homological, using connected coverings and spectral sequences.



Hide All
1Araki, S.. Cohomology modulo 2 of the compact exceptional groups. J. Math. Osaka Univ. 12 (1961), 4365.
2Araki, S. and Shikata, Y.. Cohomology mod 2 of the compact exceptional group E 8. Proc. Japan Acad. 57 (1961), 619622.
3Borel, A.. Sur l'homologie et la cohomologie des groupes de Lie compacts connexes. Amer. J. Math. 76 (1954), 273342.
4Bott, R.. An application of the Morse theory to the topology of Lie groups. Bull. Soc. Math. France 84 (1956), 251281.
5Bott, R.. The space of loop on Lie groups. Michigan Math. J. 5 (1955), 3561.
6Browder, W.. On differential Hopf algebras. Trans. Amer. Math. Soc. 107 (1963), 153176.
7Clarke, F., On the K-theory of the loop space on a Lie group. Proc. Camb. Phil. Soc. 76 (1974), 120.
8Kachi, H.. Homotopy groups of Lie groups E 6, E 7 and E 8. Nagoya Math. J. 32 (1968), 109139.
9Kono, A.. Hopf algebra structure and cohomology operation of the mod 2 cohomology of exceptional Lie groups. Japan. J. Math. (N.S.) 3 (1977), 4955.
10Milnor, J. and Moore, J. C.. On the structure of Hopf algebra. Ann. of Math. (2) 81 (1965), 211264.
11Ohshita, A.. On H-spaces with the mod 2 cohomology isomorphic to H * (Spin(n)). J. Math. Kyoto Univ. (to appear).
12Rector, D. L.. Steenrod operations in the Eilenberg-Moore spectral sequence. Comment. Math. Helv. 45 (1970), 540552.
13Rothenberg, M. and Steenrod, N.. The cohomology of the classifying spaces of H-spaces. Bull. Amer. Math. Soc. (N.S.) 71 (1961), 872875.
14Serre, J. P.. Groupes d'homotopie et classes de groupes abeliens. Ann. of Math. (2) 58 (1953), 258294.
15Thomas, E.. Exceptional Lie groups and Steenrod squares. Michigan Math. J. 11 (1964), 151156.
16Toda, H.. Composition Methods in Homotopy Groups of Spheres. Ann. of Math. Studies 49 (Princeton, NJ: Princeton University Press, 1962).
17Watanabe, T.. Cohomology operations in the loop space of the compact exceptional group F 4. Osaka J. Math. 16 (1979), 471478.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed