Generalized Gottlieb and Whitehead center groups of space forms

TL;DR

This paper extends known results on Gottlieb groups to generalized versions for space forms, providing computations and estimates for these groups for certain maps and finite groups.

Contribution

It generalizes Oprea's results to the first generalized Gottlieb group and computes or estimates higher groups for space forms with finite groups.

Findings

Extended Oprea's result to generalized Gottlieb groups.

Computed or estimated higher Gottlieb and Whitehead center groups.

Provided new insights into the structure of these groups for 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 $f\colon A\to \mathbb{S}^{2n+1}/H$. 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 $H$.