#### Volume 5, issue 1 (2001)

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The size of triangulations supporting a given link

### Simon A King

Geometry & Topology 5 (2001) 369–398
 arXiv: math.GT/0007032
##### Abstract

Let $\mathsc{T}$ 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 $\mathsc{T}$ 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