2020/01/17 by Jones, Keith, Kelsey, Gregory A.
#05C25 #20E22 #20F65 #20F69 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2001.06411
Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT(0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or not the relation of one boundary point being included in a star of another boundary point is symmetric. This paper provides an example demonstrating that this relation in the star boundary of the three-tree Diestel-Leader graph DL3(q) is not symmetric. In doing so, some interesting bounds on distance in Diestel-Leader graphs are utilized.