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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Right-angled Artin group boundaries
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by Michael Ben-Zvi and Robert Kropholler PDF
Proc. Amer. Math. Soc. 149 (2021), 555-567 Request permission


In all known examples of a CAT(0) group acting on CAT(0) spaces with non-homeomorphic CAT(0) visual boundaries, the visual boundaries are each not path-connected. In this paper, we show this does not have to be the case. In particular, for each $n>0$ we provide examples of right-angled Artin groups which exhibit non-unique CAT(0) visual boundaries where all of the visual boundaries are $n$-connected. We also prove a combination theorem for certain amalgams of CAT(0) groups to act on spaces whose visual boundaries are not path-connected. We apply this theorem to some right-angled Artin groups.
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Additional Information
  • Michael Ben-Zvi
  • Affiliation: Department of Mathematics, Bowdoin College, 8600 College Station, Brunswick, Maine 04011-8486
  • MR Author ID: 1232496
  • Email:
  • Robert Kropholler
  • Affiliation: Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstrasse 62, 48149 Münster, Deutschland
  • MR Author ID: 1178907
  • Email:
  • Received by editor(s): October 22, 2019
  • Received by editor(s) in revised form: June 2, 2020
  • Published electronically: December 9, 2020
  • Communicated by: David Futer
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 555-567
  • MSC (2010): Primary 20F65, 20F67, 57M07
  • DOI:
  • MathSciNet review: 4198064