The Triple-Point Spectrum of Closed Orientable 3-Manifolds

Abstract

The triple-point numbers and the triple-point spectrum of a closed 3-manifold are topological invariants that give a measure of the complexity of the 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.