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Duality in homotopy theory

Published online by Cambridge University Press:  26 February 2010

E. H. Spanier  and
J. H. C. Whitehead
E. H. Spanier
Affiliation:
University of Chicago. Magdalen College, Oxford
J. H. C. Whitehead
Affiliation:
University of Chicago. Magdalen College, Oxford
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Certain results ([7], [8], [10], [11]) suggest that there should be some principle of duality in homotopy theory. Among other things one is led to expect that cohomotopy groups will appear as dual to homotopy groups. But the fact that a cohomotopy group πn(X), unlike πn(X), is only defined if dim X ≤ 2n—2 is a serious obstacle to the formulation of such a principle. However, the set of S-maps (i.e.S-homotopy classes [11]) X → Y is a group for every pair of spaces X, Y. Therefore, this difficulty does not appear in S-theory [11].

Type
Research Article
Information
Mathematika , Volume 2 , Issue 1 , June 1955 , pp. 56 - 80
Copyright
Copyright © University College London 1955

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References

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