SIMPLICIAL STRUCTURES OF KNOT COMPLEMENTS

Abstract. It was shown in [7] 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.

Back to the publication list of Aleksandar Mijatović.