Homogeneity of dynamically defined wild knots

Details Homogeneity of dynamically defined wild knots Homogeneity of dynamically defined wild knots

2005-08-26

arxiv.org/abs/math/0508540v1

Mathematics

Geometric Topology

Accepted in Revista Matematica Complutense

Scientific paper

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 $p, q\in{K}$ 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.

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