✦ LIBER ✦
Topological automorphisms of modified Sierpiński gaskets realize arbitrary finite permutation groups
✍ Scribed by Reinhard Winkler
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 71 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
The n-dimensional Sierpiński gasket X, spanned by n + 1 vertices, has (n + 1)! symmetries acting as the symmetric group on the vertices. The object of this note is the remarkable observation that for n 2 every topological automorphism of X is one of these symmetries. A modification of the arguments yields that, given any finite permutation group G S n+1 acting on an (n + 1)-element set, there is a finite subset T ⊆ X such that G is the group of topological automorphisms of X \ T considered as a group acting faithfully on the vertices.