The Triple Point Spectrum of closed orientable 3-manifolds
  The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representaci\'on de 3-variedades por esferas de Dehn rellenantes, PhD Thesis, UNED 2006). They are topological invariants that give a measure of the complexity of a 3-manifold using the number of triple points of minimal filling Dehn surfaces. Basic properties of these invariants are presented, and the triple point spectra of $\mathbb{S}^2\times \mathbb{S}^1$ and $\mathbb{S}^3$ are computed. 
\'Alvaro Lozano Rojo, Rub\'en Vigara Benito
math.GT