Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem"

TL;DR

This corrigendum corrects a false corollary in a previous geometric proof of the Karpelevich-Mostow theorem, providing a counterexample and a simplified proof avoiding the invalid corollary.

Contribution

It identifies an error in the original proof, supplies a counterexample, and offers a revised, simpler proof of the theorem.

Findings

Counterexample disproves Corollary 2.3

Simplified proof of the Karpelevich-Mostow theorem

Discussion of the original proof's approach

Abstract

Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the original proof by Karpelevich.