Beben, Piotr and Theriault, Stephen
(2013)
The Kahn-Priddy Theorem and the homotopy of the three-sphere.
*Proceedings of the American Mathematical Society*, 141 (2), 711-723.

## Abstract

Let p be an odd prime. The least nontrivial p-torsion homotopy group of S^{3} occurs in dimension 2p and is of order p. This induces a map f\colon P^2p+1(p)\rightarrow S^3, where P^2p+1(p) is a mod-p Moore space. An important conjecture related to the Kahn-Priddy Theorem is that the double loops on the three-connected cover of f has a right homotopy inverse. We prove a weaker but still useful property: if X is the cofiber of f, then the double loop on the three-connected cover of the inclusion S^3\rightarrow X is null homotopic.

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