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Right-angled Artin group boundaries


Authors: Michael Ben-Zvi and Robert Kropholler
Journal: Proc. Amer. Math. Soc. 149 (2021), 555-567
MSC (2010): Primary 20F65, 20F67, 57M07
DOI: https://doi.org/10.1090/proc/15261
Published electronically: December 9, 2020
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Abstract: 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
Email: mbenzvi@bowdoin.edu

Robert Kropholler
Affiliation: Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstrasse 62, 48149 Münster, Deutschland
Email: robertkropholler@gmail.com

DOI: https://doi.org/10.1090/proc/15261
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
Article copyright: © Copyright 2020 American Mathematical Society