From Self-Similar Structures to Self-Similar Groups
Group Theory
2010-11-23 v2
Abstract
We explore the relationship between limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition such that this self-similar structure is p.c.f. We then give the necessary and sufficient condition on a p.c.f. self-similar structure such that there exists a contracting group whose limit space has an isomorphic self-similar structure; in this case, we provide a construction that produces such a contracting group. Finally, we illustrate our results with several examples.
Cite
@article{arxiv.1011.1817,
title = {From Self-Similar Structures to Self-Similar Groups},
author = {Daniel J. Kelleher and Benjamin A. Steinhurst and Chuen-Ming M. Wong},
journal= {arXiv preprint arXiv:1011.1817},
year = {2010}
}
Comments
24 pages, 11 figures