The Triple Point Spectrum of closed orientable 3-manifolds

Abstract

The triple point numbers and the triple point spectrum of a closed 3-manifold were defined in (R. Vigara, Representación 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.

arXiv comment16 pages, 11 figures