Lifting to mod 2 Moore spaces

Dedicated to the memory of Professor Katsuo Kawakubo

Abstract

We try to investigate whether an element of order 2 in homotopy groups of spheres has a lift to an element of homotopy groups of mod 2 Moore spaces or not. A typical element of the affirmative property is Thomeier's element of π_8n+7(S⁴ⁿ⁺³). And the Whitehead square [ι_2n+1, ι_2n+1] of the identity class ι_2n+1 of S²ⁿ⁺¹ is a negative example except for n=0, 1 and 3.