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arXiv · 2001.06411

On the asymmetry of stars at infinity

Keith Jones·Gregory A. Kelsey
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Abstract

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 $DL_3(q)$ is not symmetric. In doing so, some interesting bounds on distance in Diestel-Leader graphs are utilized.

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Keith Jones, Gregory A. Kelsey. 2020-01-17. On the asymmetry of stars at infinity. https://arxiv.org/abs/2001.06411

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