Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-07-02T04:09:30.705Z Has data issue: false hasContentIssue false
  • English
  • Français

On homotopy Abelian H-spaces

Published online by Cambridge University Press:  24 October 2008

James Stasheff
James Stasheff
Affiliation:
University of Oxford and Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider H-spaces which are Abelian ‘up to homotopy’ (cf. (9)). We analyse this condition in terms of the homotopy of an associated space called ‘the projective plane’. The analysis is applied to show that ΩCP(3) is homotopy Abelian.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 4 , October 1961 , pp. 734 - 745
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Barratt, M. G., James, I. M. and Stein, N., Whitehead products and projective spaces. J. Math. Mech. 9 (1960), 813–19.Google Scholar
(2)Borel, A. and Hirzebruch, F., Characteristic classes and homogeneous spaces, I. Amer. J. Math. 80 (1958), 458–538.CrossRefGoogle Scholar
(3)Dold, A. and Lashof, R., Principal quasifibrations and fibre homotopy equivalence of bundles. Illinois J. Math. 3 (1959), 285–305.CrossRefGoogle Scholar
(4)Hilton, P. J., Homotopy theory and duality (mimeographed) (Cornell University, 1959).Google Scholar
(5)Hilton, P. J., On divisors and multiples of continuous maps. Fund. Math. 43 (1956), 358–86.Google Scholar
(6)Hirzebruch, F., Über die quatemionalen projektiven Räume. S.B. bayer Akad. Wiss. (1953), pp. 301–12.Google Scholar
(7)James, I. M., On H-spaces and their homotopy groups. Quart. J. Math. (2), 11 (1960), 161–79.CrossRefGoogle Scholar
(8)James, I. M., Reduced product spaces. Ann. Math. 62 (1953), 170–97.CrossRefGoogle Scholar
(9)James, I. M. and Thomas, E., Which Lie groups are homotopy-abelian? Proc. Nat. Acad. Sci., Wash., 45 (1959), 737–40.CrossRefGoogle ScholarPubMed
(10)James, I. M. and Whitehead, J. H. C., The homotopy theory of sphere bundles over spheres (I). Proc. Lond. Math. Soc. (3), 4 (1954), 196–218.CrossRefGoogle Scholar
(11)Milnor, J., Construction of universal bundles, II. Ann. Math. 63 (1956), 430–6.CrossRefGoogle Scholar
(12)Milnor, J., The construction FK (mimeographed) (Princeton, 1956).Google Scholar
(13)Milnor, J., On spaces having the homotopy type of CW-complexes. Trans. Amer. Math. Soc. 90 (1959), 272–80.Google Scholar
(14)Samelson, H., Groups and spaces of loops. Comment. Math. Helv. 28 (1954), 278–87.CrossRefGoogle Scholar
(15)Sugawara, M., H-spaces and spaces of loops. Math. J. Okayama Univ. 5 (1955), 5–11.Google Scholar
(16)Sugawara, M., On a condition that a space is an H-space. Math. J. Okayama Univ. 6 (1957), 109–29.Google Scholar
(17)Nomura, Y., On mapping sequences. Nagoya Math. J. 17 (1960), 111–45.CrossRefGoogle Scholar