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A CAT(0) group with uncountably many distinct boundaries

Published/Copyright: July 27, 2005
Journal of Group Theory
From the journal Volume 8 Issue 2

Abstract

Croke and Kleiner [5] gave a construction for a family {Xα : 0 < α ≤ π/2} of CAT(0) spaces that each admit a geometric action by the same group G. They showed that ∂Xα ≉ ∂Xπ/2 for all α < π/2. We show that in fact ∂Xα ≉ ∂Xβ for all α ≠ β, so that G is a CAT(0) group with uncountably many non-homeomorphic boundaries.

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Published Online: 2005-07-27
Published in Print: 2005-03-08

© de Gruyter

Articles in the same Issue

  1. Coxeter covers of the symmetric groups
  2. The X-Dirichlet polynomial of a finite group
  3. On non-commuting sets in an extraspecial p-group
  4. The torsion subgroup of p-adic analytic pro-p groups
  5. Milnor groups and (virtual) nilpotence
  6. Anomalous behavior of the Hawaiian earring group
  7. A CAT(0) group with uncountably many distinct boundaries
  8. Minimal almost convexity
https://doi.org/10.1515/jgth.2005.8.2.229

Articles in the same Issue

  1. Coxeter covers of the symmetric groups
  2. The X-Dirichlet polynomial of a finite group
  3. On non-commuting sets in an extraspecial p-group
  4. The torsion subgroup of p-adic analytic pro-p groups
  5. Milnor groups and (virtual) nilpotence
  6. Anomalous behavior of the Hawaiian earring group
  7. A CAT(0) group with uncountably many distinct boundaries
  8. Minimal almost convexity
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