M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-1,
author = {Christopher Mooney},
title = {All CAT(0) boundaries of a group of the form H $\times$ K are CE equivalent},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {97-106},
zbl = {1168.57002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-1}
}
Christopher Mooney. All CAT(0) boundaries of a group of the form H × K are CE equivalent. Fundamenta Mathematicae, Tome 205 (2009) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-2-1/