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On the construction of G-spaces and applications to homogeneous spaces

Published online by Cambridge University Press:  24 October 2008

Daniel Henry Gottlieb
Daniel Henry Gottlieb
Affiliation:
Purdue University, Lafayette, Indiana
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Extract

In (3), the author defined the notion of a G-space. A G-space is a weaker notion than that of an H-space. The main purpose of this paper is to present various means of constructing G-spaces. As an application of some of the techniques of (3) and of this paper (though not an application of the concept of G-space) we shall prove the following theorem:

Theorem. Let G be a connected compact Lie group and let H be a connected subgroup of maximal rank. Then H3(G/H; Z) = 0. In fact, the Hurewicz homomorphism is trivial for odd dimensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 321 - 327
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Borel, A.Kahlerian coset spaces of semisimple Lie groups. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 1147–1151.CrossRefGoogle ScholarPubMed
(2)Bott, R.On torsion in Lie groups. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 586–588.CrossRefGoogle ScholarPubMed
(3)Gottlieb, D. H.Evaluation subgroups of homotopy groups. Amer. J. Math. 91 (1969), 729–755.CrossRefGoogle Scholar
(4)Hopf, H. and Samelson, H.Ein Satz über die Wirkungsraume geschlossener Liescher Gruppen, Comment. Math. Helv. 13 (1940–1941), 240–251.CrossRefGoogle Scholar
(5)Porter, G. J.Spaces with vanishing Whitehead Products. Quart. J. Math., Oxford, Ser (2), 16 (1965), 77–85.CrossRefGoogle Scholar
(6)Siegel, J.G-spaces, H-spaces and W-spaces. Pacific J. Math. 31 (1969), 209–213.CrossRefGoogle Scholar
(7)Wang, H. C.Homogeneous spaces with non-vanishing Euler characteristics, Ann. Math. 50 (1949), 925–953.CrossRefGoogle Scholar
(8)Haslam, H. G-spaces and H-spaces. Thesis, University of California at Irvine, 1969.Google Scholar