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Mathematische Annalen

, Volume 349, Issue 3, pp 543–575 | Cite as

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

  • Johannes Ebert
  • Jeffrey Giansiracusa
Article

Abstract

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 \({\overline{\mathfrak{M}}_{g, n}}\).

Mathematics Subject Classification (2000)

32G15 (14H15 22A22 55R40) 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany
  2. 2.Mathematical InstituteOxford UniversityOxfordUK

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