No Cover Image

Journal article 1248 views

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: Jeffrey Giansiracusa

Full text not available from this repository: check for access using links below.

Check full text

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...

Full description

Published in: Mathematische Annalen
ISSN: 0025-5831 1432-1807
Published: Springer 2011
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa7887
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2013-07-23T11:59:43Z
last_indexed 2018-02-09T04:36:34Z
id cronfa7887
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2015-07-31T17:07:54.1172566</datestamp><bib-version>v2</bib-version><id>7887</id><entry>2012-02-23</entry><title>Pontrjagin&#x2013;Thom maps and the homology of the moduli stack of stable curves</title><swanseaauthors><author><sid>03c4f93e1b94af60eb0c18c892b0c1d9</sid><firstname>Jeffrey</firstname><surname>Giansiracusa</surname><name>Jeffrey Giansiracusa</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2012-02-23</date><deptcode>FGSEN</deptcode><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.</abstract><type>Journal Article</type><journal>Mathematische Annalen</journal><volume>349</volume><journalNumber>3</journalNumber><paginationStart>543</paginationStart><paginationEnd>575</paginationEnd><publisher>Springer</publisher><issnPrint>0025-5831</issnPrint><issnElectronic>1432-1807</issnElectronic><keywords>moduli of curves, stack, homology, Potrjagin-Thom</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2011</publishedYear><publishedDate>2011-12-31</publishedDate><doi>10.1007/s00208-010-0518-2</doi><url>http://www.springerlink.com/content/p5761g1t781q3640</url><notes></notes><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2015-07-31T17:07:54.1172566</lastEdited><Created>2012-02-23T17:02:22.0000000</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Johannes</firstname><surname>Ebert</surname><order>1</order></author><author><firstname>Jeffrey</firstname><surname>Giansiracusa</surname><order>2</order></author></authors><documents/><OutputDurs/></rfc1807>
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 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-02-23 FGSEN 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 Science and Engineering - Faculty COLLEGE CODE FGSEN 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 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
active_str 0
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 2011-12-31T03:09:53Z
_version_ 1763749913849495552
score 11.016258

Similar Items