Abstract

It is not known whether there exists a computable function bounding the number of Pachner moves needed to connect any two triangulations of a compact 3-manifold. In this paper we find an explicit bound of this kind for all Haken 3-manifolds that 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 nonfibred knot complement among all 3-manifolds.

Keywords

Haken 3-manifold, triangulation, hierarchy, Pachner moves

Mathematical Subject Classification

Primary: 57N12, 57Q15

Authors