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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; mihalik@math.vanderbilt.edu, ruane@math.vanderbilt.edu
KIM RUANE
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA; mihalik@math.vanderbilt.edu, ruane@math.vanderbilt.edu
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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.

Information

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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