Erratum on "Hadamard spaces with isolated flats"

TL;DR

This paper issues an erratum to correct and clarify the proof of a key theorem in a previous work on Hadamard spaces with isolated flats, extending the results to a more general setting.

Contribution

It provides a corrected proof and detailed account of a theorem extending CAT(0) space results to broader contexts beyond flats.

Findings

Corrected proof of Theorem A.0.1

Extension of results to non-flat isolated subspaces

Enhanced understanding of CAT(0) spaces with isolated flats

Abstract

The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats'' math.GR/0411232, which was jointly authored by Mohamad Hindawi, Hruska and Kleiner. In that appendix, many of the results of math.GR/0411232 about CAT(0) spaces with isolated flats are extended to a more general setting in which the isolated subspaces are not necessarily flats. However, one step of that extension does not follow from the argument we used the isolated flats setting. We provide a new proof that fills this gap. In addition, we give a more detailed account of several other parts of Theorem A.0.1, which were sketched in math.GR/0411232.