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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Busemann points of infinite graphs


Authors: Corran Webster and Adam Winchester
Journal: Trans. Amer. Math. Soc. 358 (2006), 4209-4224
MSC (2000): Primary 20F65; Secondary 46L87, 53C23
Published electronically: April 11, 2006
MathSciNet review: 2219016
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Abstract: We provide a geometric condition which determines whether or not every point on the metric boundary of a graph with the standard path metric is a Busemann point, that is, it is the limit point of a geodesic ray. We apply this and a related condition to investigate the structure of the metric boundary of Cayley graphs. We show that groups such as the braid group and the discrete Heisenberg group have boundary points of the Cayley graph which are not Busemann points when equipped with their usual generators.


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Additional Information

Corran Webster
Affiliation: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154
Email: cwebster@unlv.nevada.edu

Adam Winchester
Affiliation: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, Nevada 89154
Address at time of publication: Department of Mathematics, University of California–Los Angeles, Box 951555, Los Angeles, California 90095-1555
Email: lagwadam@math.ucla.edu

DOI: https://doi.org/10.1090/S0002-9947-06-03877-3
Keywords: Busemann point, Cayley graph, group C*-algebra, quantum metric space
Received by editor(s): September 5, 2003
Received by editor(s) in revised form: September 28, 2004
Published electronically: April 11, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.