Modified Hanoi Towers Groups and Limit Spaces

Details Modified Hanoi Towers Groups and Limit Spaces Modified Hanoi Towers Groups and Limit Spaces

2009-09-18

arxiv.org/abs/0909.3520v1

Mathematics

Group Theory

28 Pages, 6 Figures

Scientific paper

We introduce the $k$-peg Hanoi automorphisms and Hanoi self-similar groups, a generalization of the Hanoi Towers groups, and give conditions for them to be contractive. We analyze the limit spaces of a particular family of contracting Hanoi groups, $H_c^{(k)}$, and show that these are the unique maximal contracting Hanoi groups under a suitable symmetry condition. Finally, we provide partial results on the contraction of Hanoi groups with weaker symmetry.

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