Homeomorphisms of fractafolds
Volume 209 / 2010
Fundamenta Mathematicae 209 (2010), 177-191
MSC: Primary 28A80.
DOI: 10.4064/fm209-2-5
Abstract
We classify all homeomorphisms of the double cover of the Sierpiński gasket in $n$ dimensions. We show that there is a unique homeomorphism mapping any cell to any other cell with prescribed mapping of boundary points, and any homeomorphism is either a permutation of a finite number of topological cells or a mapping of infinite order with one or two fixed points. In contrast we show that any compact fractafold based on the level-3 Sierpiński gasket is topologically rigid.
