Spines, Heegaard Splittings and the Reidemeister-Turaev Torsion

Abstract

In this article, we introduce a formula for the Reidemeister-Turaev torsion $\tau^{\varphi}(M, [\mathcal{V}], \mathfrak{o}_M)$ of an arbitrary closed 3-manifold $M$ equipped with a Spin$^c$ structure $[\mathcal{V}]$. As a CW-structure of $M$ needed in the process of the computation, we adopt the one induced from a Heegaard splitting which is compatible, via the concept of flow-spine, with a given Spin$^c$ structure.