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

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

2007-12-05

arxiv.org/abs/0712.0702v2

Mathematics

Algebraic Topology

30 pages, 3 figures - v2: expanded material on homotopy types of stacks, extended Pontrjagin-Thom construction to all local qu

Scientific paper

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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