From Self-Similar Structures to Self-Similar Groups

Daniel J. Kelleher; Benjamin A. Steinhurst; Chuen-Ming M. Wong

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arXiv · 1011.1817

From Self-Similar Structures to Self-Similar Groups

Daniel J. Kelleher·Benjamin A. Steinhurst·Chuen-Ming M. Wong

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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.

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BibTeX RIS

Daniel J. Kelleher, Benjamin A. Steinhurst, Chuen-Ming M. Wong. 2010-11-08. From Self-Similar Structures to Self-Similar Groups. https://arxiv.org/abs/1011.1817

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