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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-5,
author = {Ying Ying Chan and Robert S. Strichartz},
title = {Homeomorphisms of fractafolds},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {177-191},
zbl = {1219.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-5}
}
Ying Ying Chan; Robert S. Strichartz. Homeomorphisms of fractafolds. Fundamenta Mathematicae, Tome 209 (2010) pp. 177-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-5/