In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.
@article{urn:eudml:doc:40877,
title = {Homogeneity of dynamically defined wild knots.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {101-111},
zbl = {1120.57008},
mrnumber = {MR2219822},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40877}
}
Hinojosa, Gabriela; Verjovsky, Alberto. Homogeneity of dynamically defined wild knots.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 101-111. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40877/