All CAT(0) boundaries of a group of the form H×K are CE equivalent

Christopher Mooney
2009 Fundamenta Mathematicae  
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. 2000 Mathematics Subject Classification: 57M07, 20F65, 54C56.
doi:10.4064/fm203-2-1 fatcat:xxorul5lingeteeqvdcwge4beu