Reidemeister-Turaev torsion modulo one of rational homology threespheres.
Resolutions of moduli spaces and homological stability
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.
Riemann surfaces and spin structures