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    Bounds on Pachner moves for non-fibred Haken 3-manifolds

    Aleksandar Mijatovic
    ( Click here for pdf version )

    It has been known for some time that any triangulation of a given 3-manifold $M$ can be transformed into any other triangulation of $M$ by a finite sequence of Pachner moves. It is also known that the existence of a computable upper bound on the length of this sequence is equivalent to an algorithmic solution of the recognition problem for $M$ among all 3-manifolds.

    In this talk I will outline a string of results that lead to an explicit upper bound on the number of Pachner moves required to connect any two triangulations of $M$. The bound is in terms of the number of 3-simplices contained in the triangulations. The assumption on $M$ is that it is Haken and that none of the simple pieces of its JSJ-decomposition are homeomorphic to surface bundles or surface semi-bundles.