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Pontrjagin–Thom maps and the homology of the moduli stack of stable curves / Johannes Ebert; Jeffrey Giansiracusa

Mathematische Annalen, Volume: 349, Issue: 3, Pages: 543 - 575

Swansea University Author: Giansiracusa, Jeffrey

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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...

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Published in: Mathematische Annalen
ISSN: 0025-5831 1432-1807
Published: Springer 2011
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URI: https://cronfa.swan.ac.uk/Record/cronfa7887
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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.
Keywords: moduli of curves, stack, homology, Potrjagin-Thom
College: College of Science
Issue: 3
Start Page: 543
End Page: 575