Generalized Gottlieb and Whitehead center groups of space forms

Abstract

We extend the Oprea's result $G_1({\mathbb{S}}^{2n+1}/H)=\mathcal{Z}H$ to the 1st generalized Gottlieb group $G_1^f({\mathbb{S}}^{2n+1}/H)$ for a map $f:A\to {\mathbb{S}}^{2n+1}/H$. Then, we compute or estimate the groups $G_m^f({\mathbb{S}}^{2n+1}/H)$ and $P_m^f({\mathbb{S}}^{2n+1}/H)$ for some $m>1$ and finite groups $H$.