All ${\rm {CAT(0)}}$ boundaries of a group of the form $H\times K$ are CE equivalent
Volume 203 / 2009
Fundamenta Mathematicae 203 (2009), 97-106
MSC: 57M07, 20F65, 54C56.
DOI: 10.4064/fm203-2-1
Abstract
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.
