Gottlieb groups of spheres

This paper takes up the systematic study of the Gottlieb groups Gn+k(Sn)Gn+k(Sn) of spheres for k≤13k≤13 by means of the classical homotopy theory methods. We fully determine the groups Gn+k(Sn)Gn+k(Sn) for k≤13k≤13 except for the 2-primary components in the cases: k=9,n=53;k=11,n=115k=9,n=53;k=11,n=115. In particular, we show [ιn,ηn2σn+2]=0 if n=2i−7n=2i−7 for i≥4i≥4.