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arXiv · 0712.0702

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

Johannes Ebert·Jeffrey Giansiracusa
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Abstract

We study the singular homology (with field coefficients) of the moduli stack of stable n-pointed complex curves of genus g (the Deligne-Mumford compactification). Each of its irreducible boundary components determines via the Pontrjagin-Thom construction a map 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 implies the existence of many new torsion classes in the homology of the moduli stack.

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Johannes Ebert, Jeffrey Giansiracusa. 2008-04-23. Pontrjagin-Thom maps and the homology of the moduli stack of stable curves. https://arxiv.org/abs/0712.0702

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