Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Unstable families related to the image of J

Brayton Graya1

a1 University of Illinois at Chicago

The object of this paper is to describe certain families of unstable elements in the homotopy groups of spheres at an odd prime. In so doing we completely account for the image of J as possible Hopf invariants of unstable elements. The analogous result for p = 2 was obtained in [13]. In addition we will discuss other periodic phenomena. Our main results have been independently obtained by Bendersky[5] using BP*. Our methods, however, are entirely geometric, and we actually construct the elements, rather than detect them. Our basic tool is the map S0305004100061971_inline1.All our constructions are made in BΣp and transferred over.

(Received July 12 1983)

(Revised January 23 1984)