Triangulations of fibre-free Haken 3-manifolds

Aleksandar Mijatović

Vol. 219 (2005), No. 1, 139–186

DOI: 10.2140/pjm.2005.219.139

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 2000

Primary: 57N12, 57Q15

Milestones

Received: 19 April 2003

Revised: 29 May 2004

Published: 1 March 2005