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.
|