Lifting to mod 2 Moore spaces

摘要

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(S~4n+3). And the Whitehead square [l_2n+1,l_2n+1] of the identity class l_2n+1 of S~2n_1 is a negative example except for n=0,1 and 3.