Cyclic coverings of the 3-sphere branched over wild knots of dynamically defined type.

Let K be a tame knot and consider an n beaded necklace T ∘ which is the union of n consecutive disjoint closed round balls (pearls) B j , j = 1 , ... , n. An n pearl chain necklace T is the union of T ∘ and K. We will construct, via the action of a Kleinian group, a sequence of nested pearl chain necklaces T k whose inverse limit is a wild knot of dynamically defined type Λ (K , T 0). In this paper, we will prove some topological properties of this kind of wild knots; in particular, we generalize the construction of cyclic branched coverings for this case, and we show that there exists a wild knot of dynamically defined type such that 3 is an n -fold cyclic branched covering of 3 along it, for n ≥ 2. [ABSTRACT FROM AUTHOR]