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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Wild knots in higher dimensions as limit sets of Kleinian groups


Authors: Margareta Boege, Gabriela Hinojosa and Alberto Verjovsky
Journal: Conform. Geom. Dyn. 13 (2009), 197-216
MSC (2000): Primary 57M30; Secondary 57M45, 57Q45, 30F40
Published electronically: September 9, 2009
MathSciNet review: 2540704
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Abstract: In this paper we construct infinitely many wild knots, $ \mathbb{S}^{n}\hookrightarrow\mathbb{S}^{n+2}$, for $ n=1,2,3,4$ and $ 5$, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties.


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Additional Information

Margareta Boege
Affiliation: Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México. Av. Universidad s/n, Col. Lomas de Chamilpa, Cuernavaca, Morelos, México 62209
Email: margaret@matcuer.unam.mx

Gabriela Hinojosa
Affiliation: Facultad de Ciencias, Universidad Autónoma del Estado de Morelos. Av. Universidad 1001, Col. Chamilpa. Cuernavaca, Morelos, México 62209
Email: gabriela@buzon.uaem.mx

Alberto Verjovsky
Affiliation: Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad s/n, Col. Lomas de Chamilpa, Cuernavaca, Morelos, México 62209
Email: alberto@matcuer.unam.mx

DOI: http://dx.doi.org/10.1090/S1088-4173-09-00198-2
PII: S 1088-4173(09)00198-2
Keywords: Wild knots, Kleinian groups
Received by editor(s): May 6, 2008
Published electronically: September 9, 2009
Additional Notes: The first author’s research was partially supported by PFAMU-DGAPA
The second author’s research was partially supported by CONACyT CB-2007/83885
The third author’s research was partially supported by CONACyT proyecto U1 55084, and PAPIIT (Universidad Nacional Autónoma de México) #IN102108
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.