Sticky Cantor sets in ℝd

A subset of [Formula: see text] is called “sticky” if it cannot be isotoped off of itself by a small ambient isotopy. Sticky wild Cantor sets are constructed in [Formula: see text] for each [Formula: see text].

FOX-ARTIN ARC AND CONSTRUCTING KLEINIAN GROUPS ACTING ON S3 WITH LIMIT SET A WILD CANTOR SET

We construct purely loxodromic, geometrically finite, free Kleinian groups acting on S3 whose limit sets are wild Cantor sets. Our construction is closely related to the construction of the wild Fox–Artin arc.