A Heegaard-type presentation of branched spines and the Reidemeister–Turaev torsion

Branched spines of three-manifolds can be used to represent the homotopy class of vector fields on the ambient manifolds. In this paper, we introduce a way to present branched spines as Heegaard-type diagrams, punctured Heegaard diagrams, and explain a way to compute the Reidemeister–Turaev torsion using these diagrams.