Geometry & Topology, Vol. 5 (2001) Paper no. 13, pages 369--398.

The size of triangulations supporting a given link

Simon A King

Abstract. Let T be a triangulation of S^3 containing a link L in its 1-skeleton. We give an explicit lower bound for the number of tetrahedra of T in terms of the bridge number of L. Our proof is based on the theory of almost normal surfaces.

Keywords. Link, triangulation, bridge number, Rubinstein-Thompson algorithm, normal surfaces

AMS subject classification. Primary: 57M25, 57Q15. Secondary: 68Q25.

DOI: 10.2140/gt.2001.5.369

E-print: arXiv:math.GT/0007032

Submitted to GT on 12 September 2000. Paper accepted 8 April 2001. Paper published 20 April 2001.

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Simon A King
Institut de Recherche Mathematique Avancee
Strasbourg, France

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