Gottlieb and Whitehead center groups of projective spaces

TL;DR

This paper uses classical homotopy theory techniques to determine certain Gottlieb and Whitehead center groups of projective spaces, providing new insights into their algebraic topology structure.

Contribution

It introduces new calculations and bounds for Gottlieb and Whitehead center groups of projective spaces using Siegel's method and properties of Whitehead products.

Findings

Determined some Gottlieb groups of projective spaces.

Established lower bounds for the orders of these groups.

Identified some Whitehead center groups of projective spaces.

Abstract

By use of Siegel's method and the classical results of homotopy groups of spheres and Lie groups, we determine some Gottlieb groups of projective spaces or give the lower bounds of their orders. Furthermore, making use of the properties of Whitehead products, we determine some Whitehead center groups of projective spaces.