Gottlieb groups of spheres

Abstract

This paper takes up the systematic study of the Gottlieb groups $G_{n+k}({\S }^n)$ of spheres for $k\le 13$ by means of the classical homotopy theory methods. The groups $G_{n+k}({\S }^n)$ for $k\le 7$ and $k=10,12,13$ are fully determined. Partial results on $G_{n+k}({\S }^n)$ for $k=8,9,11$ are presented as well. We also show that $[{\iota }_n,{\eta }_n^2{\sigma }_{n+2}]=0$ if $n=2^i-7$ for $i\ge 4$.

38 pages