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