Vol. 4, No. 2, 2011
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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
The visual boundary of ℤ2

Kyle Kitzmiller and Matt Rathbun
Vol. 4 (2011), No. 2, 103–116
DOI: 10.2140/involve.2011.4.103
Abstract

We introduce ideas from geometric group theory related to boundaries of groups. We consider the visual boundary of a free abelian group, and show that it is an uncountable set with the trivial topology.
Keywords
boundary, visual boundary, Cayley graph, ℤ2, geodesic ray, quasi-isometry
Mathematical Subject Classification 2000
Primary: 20F05, 20F69, 51F99
Milestones
Received: 28 April 2009
Revised: 6 March 2011
Accepted: 7 March 2011
Published: 17 January 2012
Authors
Kyle Kitzmiller
Department of Mechanical Engineering
San Diego State University
5500 Campanile Drive
San Diego, CA 92182-1323
United States
Matt Rathbun
Department of Mathematics
University of California
One Shields Ave.
Davis, CA 95616
United States		 Department of Mathematics
Huxley Building 6M33
Imperial College London, South Kensington Campus
London, SW7 2AZ
United Kingdom
http://www2.imperial.ac.uk/~mrathbun