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CAT(0) GROUPS WITH NON-LOCALLY CONNECTED BOUNDARY

Published online by Cambridge University Press:  01 December 1999

MICHAEL MIHALIK  and
KIM RUANE
MICHAEL MIHALIK
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA; [email protected], [email protected]
KIM RUANE
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA; [email protected], [email protected]
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Abstract

The main theorem shows that whenever certain amalgamated products act geometrically on a CAT(0) space, the space has non-locally connected boundary. One can now easily construct a wide variety of examples of one-ended CAT(0) groups with non-locally connected boundary. Applications of this theorem to right-angled Coxeter and Artin groups are considered. In particular, it is shown that the natural CAT(0) space on which a right-angled Artin group acts has locally connected boundary if and only if the group is ℤn for some n.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 3 , December 1999 , pp. 757 - 770
Copyright
The London Mathematical Society 1999

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