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Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
Mathematische Annalen, Volume: 349, Issue: 3, Pages: 543 - 575
Swansea University Author: Jeffrey Giansiracusa
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DOI (Published version): 10.1007/s00208-010-0518-2
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...
| Published in: | Mathematische Annalen |
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| ISSN: | 0025-5831 1432-1807 |
| Published: |
Springer
2011
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| Online Access: |
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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. |
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| Keywords: |
moduli of curves, stack, homology, Potrjagin-Thom |
| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
543 |
| End Page: |
575 |