Homeomorphisms of fractafolds

Volume 209 / 2010

Ying Ying Chan, Robert S. Strichartz 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.

Authors

  • Ying Ying ChanMathematics Department
    Chinese University of Hong Kong
    Shatin, Hong Kong
    e-mail
  • Robert S. StrichartzMathematics Department
    Malott Hall
    Cornell University
    Ithaca, NY 14853, U.S.A.
    e-mail

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