The visual boundary of Z^2
Kyle Kitzmiller (San Diego State University), Matt Rathbun (University, of California, Davis)
TL;DR
This paper explores the concept of the visual boundary in geometric group theory, specifically for Z^2, revealing it as an uncountable set with trivial topology, and serves as an expository overview of these ideas.
Contribution
It provides an exposition of the visual boundary of Z^2, illustrating its uncountable nature and trivial topology within geometric group theory.
Findings
The visual boundary of Z^2 is uncountable.
The boundary has trivial topology.
The paper offers an expository overview.
Abstract
We introduce ideas from geometric group theory related to boundaries of groups. This is a mostly expository paper. We consider the visual boundary of a free abelian group, and show that it is an uncountable set with the trivial topology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research