Triangulations of fibre-free Haken 3-manifolds
Aleksandar Mijatovic
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.
Create a lesson
Related papers
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The flip symmetry on Khovanov-Rozansky homology
Hongjian Yang
Families of knots that cannot be made Legendrian parametrically
Javier Martínez-Aguinaga
Branched real projective structures on surfaces and geometrisation of representations
Gianluca Faraco, Nicholas Rungi
Generating the twist subgroup of the level 2 mapping class group of a non-orientable closed surface
Ryoma Kobayashi
H-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi