TRIANGULATIONS OF FIBRE-FREE HAKEN 3-MANIFOLDS

Abstract. It is not known whether there exists a computable function bounding the number
of Pachner moves needed to connect any two triangulation of a compact 3-manifold. In this paper
we find an explicit bound of this kind for all Haken 3-manifolds which contain no fibred submanifolds
as strongly simple pieces of their JSJ-decomposition. The explicit formula for the bound is in terms of
the number of tetrahedra in the two triangulations. This implies a conceptually trivial algorithm for
recognising any non-fibred knot complement among all 3-manifolds.

Back to the publication list of Aleksandar Mijatović.