All ${\rm {CAT(0)}}$ boundaries of a group of the form $H\times K$ are CE equivalent

Volume 203 / 2009

Christopher Mooney Fundamenta Mathematicae 203 (2009), 97-106 MSC: 57M07, 20F65, 54C56. DOI: 10.4064/fm203-2-1


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.


  • Christopher MooneyDepartment of Mathematics
    2074 East Hall
    530 Church Street
    Ann Arbor, MI 48109-1043, U.S.A.

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