Resumen de Uncountably many inequivalent Lipschitz homogeneous Cantor sets in R3

Dennis Garity, Dusan Repovs, Matjaz Zeljko

• General techniques are developed for constructing Lipschitz homogeneous wild Cantor sets in R3. These techniques, along with Kauffman¿s version of the Jones polynomial and previous results on Antoine Cantor sets, are used to construct uncountably many topologically inequivalent such wild Cantor sets in R3. This use of three-dimensional finite link invariants to detect distinctness among wild Cantor sets is unexpected. These Cantor sets have the same Antoine graphs and are Lipschitz homogeneous. As a corollary, there are uncountably many topologically inequivalent Cantor sets with the same Antoine graph.