Homotopy groups of the spaces of self-maps of Lie groups

TL;DR

This paper calculates the homotopy groups of the spaces of self-maps for specific rank 2 Lie groups, using their cell structures and classical homotopy theory techniques.

Contribution

It provides explicit homotopy group computations for the self-map spaces of SU(3), Sp(2), and G_2, which were previously unknown.

Findings

Homotopy groups of self-map spaces for SU(3), Sp(2), G_2 computed.

Utilizes cell structures and standard homotopy methods.

Results extend understanding of self-maps in Lie group topology.

Abstract

We compute the homotopy groups of the spaces of self maps of Lie groups of rank 2, SU(3), Sp(2), and G_2. We use the cell structures of these Lie groups and the standard methods of homotopy theory.