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.Comment: Accepted in Revista Matematica Complutens

Hinojosa, Gabriela

Verjovsky, Alberto

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arXiv

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 &#8721; 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.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 ho mogeneous: 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

Homogeneity of dynamically defined wild knots

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