Triangulations of fibre-free Haken 3-manifolds

Aleksandar Mijatovic

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Triangulations of fibre-free Haken 3-manifolds

Aleksandar Mijatovic

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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.

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BibTeX RIS

Aleksandar Mijatovic. 2003-06-06. Triangulations of fibre-free Haken 3-manifolds. https://arxiv.org/abs/math/0306116

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