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

Johannes Ebert, Jeffrey Giansiracusa Orcid Logo

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

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

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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...

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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
first_indexed 2013-07-23T11:59:43Z
last_indexed 2018-02-09T04:36:34Z
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spelling 2015-07-31T17:07:54.1172566 v2 7887 2012-02-23 Pontrjagin–Thom maps and the homology of the moduli stack of stable curves 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-02-23 MACS 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. Journal Article Mathematische Annalen 349 3 543 575 Springer 0025-5831 1432-1807 moduli of curves, stack, homology, Potrjagin-Thom 31 12 2011 2011-12-31 10.1007/s00208-010-0518-2 http://www.springerlink.com/content/p5761g1t781q3640 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2015-07-31T17:07:54.1172566 2012-02-23T17:02:22.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Johannes Ebert 1 Jeffrey Giansiracusa 0000-0003-4252-0058 2
title Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
spellingShingle Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
Jeffrey Giansiracusa
title_short Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
title_full Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
title_fullStr Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
title_full_unstemmed Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
title_sort Pontrjagin–Thom maps and the homology of the moduli stack of stable curves
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
author Jeffrey Giansiracusa
author2 Johannes Ebert
Jeffrey Giansiracusa
format Journal article
container_title Mathematische Annalen
container_volume 349
container_issue 3
container_start_page 543
publishDate 2011
institution Swansea University
issn 0025-5831
1432-1807
doi_str_mv 10.1007/s00208-010-0518-2
publisher Springer
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://www.springerlink.com/content/p5761g1t781q3640
document_store_str 0
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description 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.
published_date 2011-12-31T03:15:31Z
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score 11.089407

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