Full paper in PDF:
$%G. Hinojosa and A. Verjovsky, Homogeneity of dynamically defined wild knots,
Rev. Mat. Complut. 19 (2006), no. 1, 101–111.%$
Universidad Autóma del Estado de Morelos Av. Universidad 1001, Col. Chamilpa 62210 Cuernavaca, Morelos — Mexico | Instituto de Matemáticas Universidad Nacional Autónoma de México Unidad Cuernavaca Av. Universidad s/n, Col. Lomas de Chamilpa 62210 Cuernavaca, Morelos — Mexico |
In this paper we prove that a wild knot
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
there exists a homeomorphism
of
the sphere such that
and
. We also show that if the wild
knot is a fibered knot then we can choose an
which preserves the fibers.
Key words: wild knots and Kleinian groups.
2000 Mathematics Subject Classification: Primary: 57M30. Secondary: 57M45, 57Q45,
30F14.