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On the homotopy type of the Deligne–Mumford compactification

Johannes Ebert, Jeffrey Giansiracusa Orcid Logo

Algebraic & Geometric Topology, Volume: 8, Issue: 4, Pages: 2049 - 2062

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

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DOI (Published version): 10.2140/agt.2008.8.2049

Abstract

An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational homology as the Deligne-Mumford compactification. We give an integral refinement: the classifying space of the Charney-Lee...

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Published in: Algebraic & Geometric Topology
ISSN: 1472-2739 1472-2747
Published: Mathematical Sciences Publishers 2008
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URI: https://cronfa.swan.ac.uk/Record/cronfa13607
first_indexed 2013-07-23T12:10:34Z
last_indexed 2018-02-09T04:44:25Z
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spelling 2011-10-01T00:00:00.0000000 v2 13607 2012-12-10 On the homotopy type of the Deligne–Mumford compactification 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-12-10 MACS An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational homology as the Deligne-Mumford compactification. We give an integral refinement: the classifying space of the Charney-Lee category actually has the same homotopy type as the moduli stack of stable curves, and the etale homotopy type of the moduli stack is equivalent to the profinite completion of the classifying space of the Charney-Lee category. Journal Article Algebraic & Geometric Topology 8 4 2049 2062 Mathematical Sciences Publishers 1472-2739 1472-2747 5 11 2008 2008-11-05 10.2140/agt.2008.8.2049 http://www.msp.warwick.ac.uk/agt/2008/08-04/p072.xhtml COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2011-10-01T00:00:00.0000000 2012-12-10T14:44:26.3895319 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Johannes Ebert 1 Jeffrey Giansiracusa 0000-0003-4252-0058 2
title On the homotopy type of the Deligne–Mumford compactification
spellingShingle On the homotopy type of the Deligne–Mumford compactification
Jeffrey Giansiracusa
title_short On the homotopy type of the Deligne–Mumford compactification
title_full On the homotopy type of the Deligne–Mumford compactification
title_fullStr On the homotopy type of the Deligne–Mumford compactification
title_full_unstemmed On the homotopy type of the Deligne–Mumford compactification
title_sort On the homotopy type of the Deligne–Mumford compactification
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 Algebraic & Geometric Topology
container_volume 8
container_issue 4
container_start_page 2049
publishDate 2008
institution Swansea University
issn 1472-2739
1472-2747
doi_str_mv 10.2140/agt.2008.8.2049
publisher Mathematical Sciences Publishers
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.msp.warwick.ac.uk/agt/2008/08-04/p072.xhtml
document_store_str 0
active_str 0
description An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational homology as the Deligne-Mumford compactification. We give an integral refinement: the classifying space of the Charney-Lee category actually has the same homotopy type as the moduli stack of stable curves, and the etale homotopy type of the moduli stack is equivalent to the profinite completion of the classifying space of the Charney-Lee category.
published_date 2008-11-05T18:27:50Z
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score 11.048042

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