The size of triangulations supporting a given link

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

Mathematical Subject Classification 2000

Primary: 57M25, 57Q15

Secondary: 68Q25

References

Forward citations

Publication

Received: 12 September 2000

Accepted: 8 April 2001

Published: 20 April 2001

Proposed: Walter Neumann

Seconded: Cameron Gordon, David Gabai

Authors

Simon A King
Institut de Recherche Mathématique Avancée Strasbourg France

Volume 5, issue 1 (2001)

Simon A King