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arXiv 1011.18172010-11-19math.GR

从自相似结构到自相似群

From Self-Similar Structures to Self-Similar Groups

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

备注：: 24 pages, 11 figures

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摘要：

我们探讨了收缩自相似群的极限空间与自相似结构之间的关系。给出了收缩群的极限空间存在自相似结构的条件，以及这种自相似结构是p.c.f.的条件。然后我们给出了p.c.f.的充要条件。自相似结构，使得存在一个收缩群，其极限空间具有同构的自相似结构;在这种情况下，我们提供了一个产生这种收缩群的构造。最后，我们用几个例子来说明我们的结果。

英文摘要：

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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