Compact groups and absolute extensors

TL;DR

This paper characterizes certain compact Lie groups as absolute extensors with specific homotopy properties, providing a converse to a classical result by R. Bott.

Contribution

It offers a new characterization of simple, connected, simply connected compact Lie groups as AE(2)-groups with a particular third homotopy group.

Findings

Characterization of simple, connected, simply connected compact Lie groups as AE(2)-groups.

Identification of the third homotopy group as Z for these groups.

Provides a converse to R. Bott's classical result.

Abstract

We discuss compact Hausdorff groups from the point of view of the general theory of absolute extensors. In particular, we characterize the class of simple, connected and simply connected compact Lie groups as AE(2)-groups the third homotopy group of which is $\text{\f Z}$. This is the converse of the corresponding result of R. Bott.