Pontrjagin-Thom maps and the homology of the moduli stack of stable curves

We study the singular homology (with field coefficients) of the moduli stack of stable n-pointed complex curves of genus g. Each irreducible boundary component of determines via the Pontrjagin-Thom construction a map from to a certain infinite loop space whose homology is well understood. We show that these maps are surjective on homology in a range of degrees proportional to the genus. This detects many new torsion classes in the homology.