Mathematical Research Letters

Volume 12 (2005)

Number 6

Simplical structures of knot complements

Pages: 843 – 856



Aleksandar Mijatovic (University of Cambridge)


It was shown in~\cite{mijatov2} that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot complements. The explicit formula for the bound is in terms of the numbers of tetrahedra in the two triangulations. This gives a conceptually trivial algorithm for recognising any knot complement among all 3-manifolds.

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