Journal article 1190 views
The framed little 2-discs operad and diffeomorphisms of handlebodies
J Giansiracusa,
Jeffrey Giansiracusa
Journal of Topology, Volume: 4, Issue: 4, Pages: 919 - 941
Swansea University Author: Jeffrey Giansiracusa
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DOI (Published version): 10.1112/jtopol/jtr021
Abstract
The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (that is, the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular operad made from classifying spaces of diffeo...
Published in: | Journal of Topology |
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ISSN: | 1753-8416 1753-8424 |
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2011
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URI: | https://cronfa.swan.ac.uk/Record/cronfa13605 |
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<?xml version="1.0"?><rfc1807><datestamp>2015-07-31T17:07:25.2570716</datestamp><bib-version>v2</bib-version><id>13605</id><entry>2012-12-10</entry><title>The framed little 2-discs operad and diffeomorphisms of handlebodies</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>2012-12-10</date><deptcode>FGSEN</deptcode><abstract>The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (that is, the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular operad made from classifying spaces of diffeomorphism groups of 3-dimensional handlebodies with marked discs on their boundaries. A modification of the argument provides a new and elementary proof of Costello's theorem that the derived modular envelope of the associative operad is homotopy equivalent to the ‘open string’ modular operad made from moduli spaces of Riemann surfaces with marked intervals on the boundary. Our technique also recovers a theorem of Braun that the derived modular envelope of the cyclic operad that describes associative algebras with involution is homotopy equivalent to the modular operad made from moduli spaces of unoriented Klein surfaces with open string gluing.</abstract><type>Journal Article</type><journal>Journal of Topology</journal><volume>4</volume><journalNumber>4</journalNumber><paginationStart>919</paginationStart><paginationEnd>941</paginationEnd><publisher/><issnPrint>1753-8416</issnPrint><issnElectronic>1753-8424</issnElectronic><keywords>handlebodies, modular envelope, operads, moduli space, cyclic operad, modular operad, graph homology, ribbon graphs, mobius graphs, framed little discs, Batalin-Vilkovisky</keywords><publishedDay>1</publishedDay><publishedMonth>11</publishedMonth><publishedYear>2011</publishedYear><publishedDate>2011-11-01</publishedDate><doi>10.1112/jtopol/jtr021</doi><url>http://jtopol.oxfordjournals.org/content/4/4/919.abstract</url><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2015-07-31T17:07:25.2570716</lastEdited><Created>2012-12-10T14:36:00.4003761</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>J</firstname><surname>Giansiracusa</surname><order>1</order></author><author><firstname>Jeffrey</firstname><surname>Giansiracusa</surname><order>2</order></author></authors><documents/><OutputDurs/></rfc1807> |
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2015-07-31T17:07:25.2570716 v2 13605 2012-12-10 The framed little 2-discs operad and diffeomorphisms of handlebodies 03c4f93e1b94af60eb0c18c892b0c1d9 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-12-10 FGSEN The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (that is, the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular operad made from classifying spaces of diffeomorphism groups of 3-dimensional handlebodies with marked discs on their boundaries. A modification of the argument provides a new and elementary proof of Costello's theorem that the derived modular envelope of the associative operad is homotopy equivalent to the ‘open string’ modular operad made from moduli spaces of Riemann surfaces with marked intervals on the boundary. Our technique also recovers a theorem of Braun that the derived modular envelope of the cyclic operad that describes associative algebras with involution is homotopy equivalent to the modular operad made from moduli spaces of unoriented Klein surfaces with open string gluing. Journal Article Journal of Topology 4 4 919 941 1753-8416 1753-8424 handlebodies, modular envelope, operads, moduli space, cyclic operad, modular operad, graph homology, ribbon graphs, mobius graphs, framed little discs, Batalin-Vilkovisky 1 11 2011 2011-11-01 10.1112/jtopol/jtr021 http://jtopol.oxfordjournals.org/content/4/4/919.abstract COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2015-07-31T17:07:25.2570716 2012-12-10T14:36:00.4003761 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics J Giansiracusa 1 Jeffrey Giansiracusa 2 |
title |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
spellingShingle |
The framed little 2-discs operad and diffeomorphisms of handlebodies Jeffrey Giansiracusa |
title_short |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
title_full |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
title_fullStr |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
title_full_unstemmed |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
title_sort |
The framed little 2-discs operad and diffeomorphisms of handlebodies |
author_id_str_mv |
03c4f93e1b94af60eb0c18c892b0c1d9 |
author_id_fullname_str_mv |
03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa |
author |
Jeffrey Giansiracusa |
author2 |
J Giansiracusa Jeffrey Giansiracusa |
format |
Journal article |
container_title |
Journal of Topology |
container_volume |
4 |
container_issue |
4 |
container_start_page |
919 |
publishDate |
2011 |
institution |
Swansea University |
issn |
1753-8416 1753-8424 |
doi_str_mv |
10.1112/jtopol/jtr021 |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
hierarchy_top_id |
facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
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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://jtopol.oxfordjournals.org/content/4/4/919.abstract |
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0 |
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0 |
description |
The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (that is, the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to the modular operad made from classifying spaces of diffeomorphism groups of 3-dimensional handlebodies with marked discs on their boundaries. A modification of the argument provides a new and elementary proof of Costello's theorem that the derived modular envelope of the associative operad is homotopy equivalent to the ‘open string’ modular operad made from moduli spaces of Riemann surfaces with marked intervals on the boundary. Our technique also recovers a theorem of Braun that the derived modular envelope of the cyclic operad that describes associative algebras with involution is homotopy equivalent to the modular operad made from moduli spaces of unoriented Klein surfaces with open string gluing. |
published_date |
2011-11-01T03:15:33Z |
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1763750270371627008 |
score |
11.012678 |