Wild Cantor sets in $R^3$: A survey.

The first part of the talk will be a historical survey on wild Cantor sets in $R^3$, the first such
set being constructed by Louis Antoine already in the 1920's in his Dissertation, after he was blinded while
serving in the French army during WWI. In the second part of the talk we shall
present a new general technique for constructing wild Cantor sets in $R^{3}$ which are nevertheless
Lipschitz homogeneously embedded into $R^3$. Applying the well-known Kauffman version of the Jones polynomial
we shall show that our construction produces even uncountably many topologically inequivalent wild
Cantor sets in $R^{3}$. These Cantor sets have the same number of components in the interior of each
stage of the defining sequence and are Lipschitz homogenous. We shall also announce some other new
results on wild Cantor sets in $R^3$ and state some related open problems and conjectures.