Boundaries of Nonpositively Curved Groups of the Form G Z Z N
نویسندگان
چکیده
We prove that whenever G is negatively curved and ? = G ZZ n acts geometrically on two CAT(0)-spaces X and X 0 , their visual boundaries are ?-equivariantly homeomorphic, answering aarmatively a question of Gromov in this special case. However, we give a simple example that shows that the natural ?-equivariant quasi-isometry from X to X 0 does not continuously extend to a homeomorphism of visual boundaries, a situation that does occur if ? is negatively curved. We show further that the ?-rational endpoints of X form a dense subset of the visual boundary, generalizing the analogous result that holds in the context of negative curvature. bnpcgfgz.tex 1 02/28/95
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