EXISTENCE OF THE STABLE HOMOTOPY FAMILY {yj
نویسندگان
چکیده
Toda [7] has asked whether Smith's K(rc)-construction for n = 3 yields a nontrivial element yx in the p-component p%% of the stable homotopy of spheres (p a prime, p ^ 5). This question has become a major stumbling block, since yt has stubbornly refused to be detected by most conventional invariants [9]. We can now show that yt is essential; moreover (for p ^ 7) it is only the first of a new family {yt} of stable homotopy elements, which are nontrivial for t ^ p — 1 at least. The family {yt} parallels the known infinite families {<xt} and {ft} ([1], [4], [8], [10], [12]). We define yt to be the composite
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