Gottlieb groups of spheres

This paper takes up the systematic study of the Gottlieb groups G n + k ( S n ) of spheres for k ≤ 13 by means of the classical homotopy theory methods. We fully determine the groups G n + k ( S n ) for k ≤ 13 except for the 2-primary components in the cases: k = 9 , n = 53 ; k = 11 , n = 115 . In particular, we show [ ι n , η n 2 σ n + 2 ] = 0 if n = 2 i − 7 for i ≥ 4 .