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We prove that there exist uncountably many inequivalent rigid wild Cantor sets in R 3 with simply connected complement. Previous constructions of wild Cantor sets in R 3 with simply connected complement, in particular the Bing-Whitehead Cantor sets, had strong homogeneity properties. This suggested it might not be possible to construct such sets that were rigid. The examples in this paper are constructed using a generalization of a construction of Skora together with a careful analysis of the local genus of points in the Cantor sets.

Rigid cantor sets in $R^3$ with simply connected complement