Gottlieb groups of spheres

Details Gottlieb groups of spheres Gottlieb groups of spheres

2004-08-19

arxiv.org/abs/math/0408256v1

Mathematics

Algebraic Topology

38 pages

Scientific paper

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 $[\iota_n,\eta^2_n\sigma_{n+2}]=0$ if $n=2^i-7$ for $i\ge 4$.

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