2003/06/06 by Aleksandar Mijatović, Aleksandar Mijatovic, Mijatovic, Aleksandar
Mathematics · #57M99 #57N10 #57Q15 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M99 #msc:57N10 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.math/0306116
30 pages, 4 figures
arxiv created 2003/06/06 · openalex publication_date 2003/06/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.