The triangulation complexity of 3-manifolds

Jessica Purcell (Monash University)


The triangulation complexity of a compact 3-manifold is the minimal number of tetrahedra required to triangulate the manifold. It is surprisingly challenging to compute. In this talk, I will describe results that compute the triangulation complexity of families of compact 3-manifolds to within a universally bounded multiplicative error, in terms of topological information obtained from the manifold. The families we consider are fibred 3-manifolds, thickened surfaces, and most recently, elliptic and sol 3-manifolds. This is joint work with Marc Lackenby.

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