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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.

Information

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

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