Adele Jackson

Triangulations of Seifert fibered spaces

To compute invariants of 3-manifolds in practice, we generally give them as triangulations. Two questions immediately arise: how large is the triangulation, and are there small representatives of the topology of the 3-manifold in it? The triangulation complexity of a 3-manifold is the minimal number of tetrahedra in a triangulation of it. This number has connections to Gromov volume and Heegaard genus, but is challenging to understand. I will give the approximate triangulation complexity of Seifert fibered spaces, which are a large class of 3-manifolds arising from geometric decomposition, by finding bounded complexity representatives of some interesting curves and surfaces in any triangulation of one.