Abstract
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].
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