Abstract
We introduce and characterize extremal 2-cuts for good fractal necklaces. Using this characterization and the related topological properties of extremal 2-cuts, we prove that every good necklace has a unique necklace IFS in a certain sense. Also, we prove that two good necklaces admit only rigid homeomorphisms and thus the group of self-homeomorphisms of a good necklace is countable. In addition, a certain weaker co-Hopfian property of good necklaces is also obtained.
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Acknowledgement
The author thanks Professors Fang Fuquan and Shigeki Akiyama for their helpful suggestions.
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Wen, F. Topological rigidity of good fractal necklaces. Acta Math. Hungar. 168, 78–94 (2022). https://doi.org/10.1007/s10474-022-01275-6
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DOI: https://doi.org/10.1007/s10474-022-01275-6