Right-angled Artin group boundaries

2019/10/16 by Ben-Zvi, Michael, Kropholler, Robert
#20F65 #20F67 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1910.07560

Abstract

In all known examples of a CAT(0) group acting on CAT(0) spaces with non-homeomorphic CAT(0) visual boundaries, the boundaries are each not path connected. In this paper, we show this does not have to be the case by providing examples of right-angled Artin groups which exhibit non-unique CAT(0) boundaries where all of the boundaries are arbitrarily connected. We also prove a combination theorem for certain amalgams of CAT(0) groups to act on spaces with non-path connected visual boundaries. We apply this theorem to some right-angled Artin groups.

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• Teoria Geometrica dei Gruppi Spazi CAT(0), Teorema di Gromov e oriented right-angled Artin groups