Abstract
A fundamental question of geometric group theory is how groups can be viewed as geometric objects; one way to view a (finitely generated) group as a geometric object is via Cayley graphs:
-
1.
As the first step, one associates a combinatorial structure to a group and a given generating set: the corresponding Cayley graph. This step already has a rudimentary geometric avour and is discussed in this chapter.
-
2.
As the second step, one adds a metric structure to Cayley graphs via word metrics. We will study this step in Chapter 5.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Löh, C. (2017). Cayley graphs. In: Geometric Group Theory. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-72254-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-72254-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72253-5
Online ISBN: 978-3-319-72254-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)