Vol. 4, No. 2, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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