|
|||||
 |
|
|
|
|
|
|
|
The visual
boundary of $\mathbb{Z}^2$
Kyle Kitzmiller and Matt Rathbun |
|
Vol. 4 (2011), No. 2, 103–116
|
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, $\mathbb Z^2$,
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
Communicated by Kenneth S. Berenhaut
|
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 | |
| © 2011 MSP (Mathematical Sciences Publishers). |
