English

Homogeneity of dynamically defined wild knots

Geometric Topology 2007-05-23 v1

Abstract

In this paper we prove that a wild knot KK 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,qKp, q\in{K} there exists a homeomorphism ff of the sphere such that f(K)=Kf(K)=K and f(p)=qf(p)=q. We also show that if the wild knot is a fibered knot then we can choose an ff which preserves the fibers.

Cite

@article{arxiv.math/0508540,
  title  = {Homogeneity of dynamically defined wild knots},
  author = {Gabriela Hinojosa and Alberto Verjovsky},
  journal= {arXiv preprint arXiv:math/0508540},
  year   = {2007}
}

Comments

Accepted in Revista Matematica Complutense