No Cover Image

Conference Paper/Proceeding/Abstract 660 views

Formality of the framed little 2-discs operad and semidirect products / Jeffrey, Giansiracusa

Contemporary Mathematics, Volume: 519, Pages: 115 - 121

Swansea University Author: Jeffrey, Giansiracusa

Abstract

We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in the category of S^1-spaces, and the framed 2-discs operad can be constructed from the unframed 2-discs by forming the oper...

Full description

Published in: Contemporary Mathematics
Published: AMS 2010
URI: https://cronfa.swan.ac.uk/Record/cronfa8376
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2013-07-23T12:00:56Z
last_indexed 2018-02-09T04:37:21Z
id cronfa8376
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2013-06-17T14:50:32.5396603</datestamp><bib-version>v2</bib-version><id>8376</id><entry>2012-02-22</entry><title>Formality of the framed little 2-discs operad and semidirect products</title><swanseaauthors><author><sid>03c4f93e1b94af60eb0c18c892b0c1d9</sid><ORCID>0000-0003-4252-0058</ORCID><firstname>Jeffrey</firstname><surname>Giansiracusa</surname><name>Jeffrey Giansiracusa</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2012-02-22</date><deptcode>SMA</deptcode><abstract>We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in the category of S^1-spaces, and the framed 2-discs operad can be constructed from the unframed 2-discs by forming the operadic semidirect product with the circle group. The idea of our proof is to show that Kontsevich&amp;apos;s chain of quasi-isomorphisms is compatible with the circle actions and so one can essentially take the operadic semidirect product with the homology of S^1 everywhere to obtain a chain of quasi-isomorphisms between the homology and the chains of the framed 2-discs.In Homotopy theory of function spaces and related topics, 115&#x2013;121, Contemp. Math., 519, Amer. Math. Soc., Providence, RI, 2010. arXiv:0911.4428</abstract><type>Conference Paper/Proceeding/Abstract</type><journal>Contemporary Mathematics</journal><volume>519</volume><journalNumber></journalNumber><paginationStart>115</paginationStart><paginationEnd>121</paginationEnd><publisher>AMS</publisher><placeOfPublication/><issnPrint/><issnElectronic/><keywords>Framed little discs, formality, semidirect product</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2010</publishedYear><publishedDate>2010-12-31</publishedDate><doi></doi><url/><notes></notes><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><lastEdited>2013-06-17T14:50:32.5396603</lastEdited><Created>2012-02-22T13:37:15.0000000</Created><path><level id="1">College of Science</level><level id="2">Mathematics</level></path><authors><author><firstname>Jeff</firstname><surname>Giansiracusa</surname><order>1</order></author><author><firstname>Paolo</firstname><surname>Salvatore</surname><order>2</order></author><author><firstname>Jeffrey</firstname><surname>Giansiracusa</surname><orcid>0000-0003-4252-0058</orcid><order>3</order></author></authors><documents/></rfc1807>
spelling 2013-06-17T14:50:32.5396603 v2 8376 2012-02-22 Formality of the framed little 2-discs operad and semidirect products 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-02-22 SMA We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in the category of S^1-spaces, and the framed 2-discs operad can be constructed from the unframed 2-discs by forming the operadic semidirect product with the circle group. The idea of our proof is to show that Kontsevich&apos;s chain of quasi-isomorphisms is compatible with the circle actions and so one can essentially take the operadic semidirect product with the homology of S^1 everywhere to obtain a chain of quasi-isomorphisms between the homology and the chains of the framed 2-discs.In Homotopy theory of function spaces and related topics, 115–121, Contemp. Math., 519, Amer. Math. Soc., Providence, RI, 2010. arXiv:0911.4428 Conference Paper/Proceeding/Abstract Contemporary Mathematics 519 115 121 AMS Framed little discs, formality, semidirect product 31 12 2010 2010-12-31 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2013-06-17T14:50:32.5396603 2012-02-22T13:37:15.0000000 College of Science Mathematics Jeff Giansiracusa 1 Paolo Salvatore 2 Jeffrey Giansiracusa 0000-0003-4252-0058 3
title Formality of the framed little 2-discs operad and semidirect products
spellingShingle Formality of the framed little 2-discs operad and semidirect products
Jeffrey, Giansiracusa
title_short Formality of the framed little 2-discs operad and semidirect products
title_full Formality of the framed little 2-discs operad and semidirect products
title_fullStr Formality of the framed little 2-discs operad and semidirect products
title_full_unstemmed Formality of the framed little 2-discs operad and semidirect products
title_sort Formality of the framed little 2-discs operad and semidirect products
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey, Giansiracusa
author Jeffrey, Giansiracusa
format Conference Paper/Proceeding/Abstract
container_title Contemporary Mathematics
container_volume 519
container_start_page 115
publishDate 2010
institution Swansea University
publisher AMS
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
document_store_str 0
active_str 0
description We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in the category of S^1-spaces, and the framed 2-discs operad can be constructed from the unframed 2-discs by forming the operadic semidirect product with the circle group. The idea of our proof is to show that Kontsevich&apos;s chain of quasi-isomorphisms is compatible with the circle actions and so one can essentially take the operadic semidirect product with the homology of S^1 everywhere to obtain a chain of quasi-isomorphisms between the homology and the chains of the framed 2-discs.In Homotopy theory of function spaces and related topics, 115–121, Contemp. Math., 519, Amer. Math. Soc., Providence, RI, 2010. arXiv:0911.4428
published_date 2010-12-31T19:18:25Z
_version_ 1667868661495365632
score 10.900483