Right-angled Artin group boundaries

Ben-Zvi, Michael; Kropholler, Robert

doi:10.1090/proc/15261

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

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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