Invariants for everywhere wild knots

Abstract

Bing, Bothe and Shilepsky studied knots that were wild at every point, and Bothe developed an invariant for a certain subclass of these knots. This paper develops invariants which distinguish ambient isotopy equivalence classes of these knots (which include the "Bing sling") and shows that there is an uncountable number of inequivalent of Bing sling type knots. As an aside, it is also shown that it is possible for inequivalent wild knots to have homeomorphic complements.