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The triangulation complexity of fibred 3-manifolds

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Jessica Purcell (Monash)

Abstract: The triangulation complexity of a 3-manifold M is the minimal number of
tetrahedra required to form a triangulation of M. It is a useful invariant, for
example in computational topology, but surprisingly difficult to compute. We
consider the case that M is a closed orientable hyperbolic 3-manifold that
fibers over the circle. We show that the triangulation complexity of such a
manifold is equal to the translation length of the monodromy action on the
mapping class group of the fibre, up to a bounded factor depending only on the
genus of the fibre. This is joint work with Marc Lackenby.