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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.
Ying Ying Chan, and Robert S. Strichartz. "Homeomorphisms of fractafolds." Fundamenta Mathematicae 209.2 (2010): 177-191. <http://eudml.org/doc/283206>.
@article{YingYingChan2010, 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.}, author = {Ying Ying Chan, Robert S. Strichartz}, journal = {Fundamenta Mathematicae}, keywords = {Sierpiński gasket; fractafold; topological rigidity}, language = {eng}, number = {2}, pages = {177-191}, title = {Homeomorphisms of fractafolds}, url = {http://eudml.org/doc/283206}, volume = {209}, year = {2010}, }
TY - JOUR AU - Ying Ying Chan AU - Robert S. Strichartz TI - Homeomorphisms of fractafolds JO - Fundamenta Mathematicae PY - 2010 VL - 209 IS - 2 SP - 177 EP - 191 AB - 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. LA - eng KW - Sierpiński gasket; fractafold; topological rigidity UR - http://eudml.org/doc/283206 ER -