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Fox coloured knots and triangulations of $S^{3}$

Published online by Cambridge University Press:  01 December 2006

HUGH M. HILDEN ,
JOSÉ M. MONTESINOS-AMILIBIA ,
DÉBORA M. TEJADA  and
MARGARITA M. TORO
HUGH M. HILDEN
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96825, U.S.A. e-mail: [email protected]
JOSÉ M. MONTESINOS-AMILIBIA
Affiliation:
Departamento de Geometría y Topología, Universidad Complutense, 28040 Madrid, Spain. e-mail: [email protected]
DÉBORA M. TEJADA
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia. e-mail: [email protected], [email protected]
MARGARITA M. TORO
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia. e-mail: [email protected], [email protected]
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Abstract

We give a constructive proof of a Theorem of Izmestiev and Joswig. Namely, given $(L,\omega)$ where $L$ is a link in $S^{3}$ and $\omega$ a simple (not necessarily transitive) representation of $\pi_{1}(S^{3}\backslash L)$ onto the symmetric group $\Sigma_{4}$ of four elements $\{1,2,3,4\}$ we construct a triangulation of $S^{3}$ giving rise to $(L,\omega)$ in a natural way.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 3 , November 2006 , pp. 443 - 463
Copyright
© 2006 Cambridge Philosophical Society

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