Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-13T02:54:20.060Z Has data issue: false hasContentIssue false
  • English
  • Français

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: mike@math.hawaii.edu
JOSÉ M. MONTESINOS-AMILIBIA
Affiliation:
Departamento de Geometría y Topología, Universidad Complutense, 28040 Madrid, Spain. e-mail: montesin@mat.ucm.es
DÉBORA M. TEJADA
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia. e-mail: dtejada@unalmed.edu.co, mmtoro@unalmed.edu.co
MARGARITA M. TORO
Affiliation:
Escuela de Matemáticas, Universidad Nacional de Colombia, Apartado Aéreo 3840, Medellín, Colombia. e-mail: dtejada@unalmed.edu.co, mmtoro@unalmed.edu.co
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)