From Self-Similar Structures to Self-Similar Groups


Daniel Kelleher, Benjamin Steinhurst, and Chuen-Ming Wong


This group explored the relationship between limit spaces of contracting self-similar groups and self-similar structures. They gave 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. They then gave 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, they provided a construction that produces such a contracting group. Finally, they illustrated their results with several examples.

International Journal of Algebra and Computation (IJAC)