分野別セミナー

Let p be an odd prime. The least nontrivial
p-torsion homotopy group of S3 occurs in dimension 2p
and has order p. This induces a map f:P --> S3,
where P is a mod-p Moore space of dimension 2p+1. A

major conjecture in unstable homotopy theory is that
the double loops on the 3-connected cover of f has a
right inverse. We prove a weaker but still useful
property: if X is the cofiber of f then the double loops

on the 3-connected cover of the inclusion S3 --> X is
null homotopic. Applications are given.