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We study the singular homology (with field coefficients) of the moduli stack $${\overline{\mathfrak{M}}_{g, n}}$$ of stable n-pointed complex curves of genus g. Each irreducible boundary component of $${\overline{\mathfrak{M}}_{g, n}}$$ determines via the Pontrjagin–Thom construction a map from $${\overline{\mathfrak{M}}_{g, n}}$$ 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 of $${\overline{\mathfrak{M}}_{g, n}}$$.

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