Resolutions of moduli spaces and homological stability

Understand

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 give 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.