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Cyclic operad formality for compactified moduli spaces of genus zero surfaces

Jeffrey Giansiracusa Orcid Logo, Paolo Salvatore

Transactions of the American Mathematical Society, Volume: 364, Issue: 11, Pages: 5881 - 5911

Swansea University Author: Jeffrey Giansiracusa Orcid Logo

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DOI (Published version): 10.1090/S0002-9947-2012-05553-X

Abstract

The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovi...

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Published in: Transactions of the American Mathematical Society
ISSN: 0002-9947 1088-6850
Published: AMS 2012
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URI: https://cronfa.swan.ac.uk/Record/cronfa8375
first_indexed 2013-07-23T12:00:55Z
last_indexed 2018-02-09T04:37:21Z
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spelling 2013-06-13T08:36:22.8723663 v2 8375 2012-02-22 Cyclic operad formality for compactified moduli spaces of genus zero surfaces 03c4f93e1b94af60eb0c18c892b0c1d9 0000-0003-4252-0058 Jeffrey Giansiracusa Jeffrey Giansiracusa true false 2012-02-22 MACS The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove this we introduce a new complex of graphs in which the differential is a combination of edge deletion and contraction, and we show that this complex resolves BV as a cyclic operad. Journal Article Transactions of the American Mathematical Society 364 11 5881 5911 AMS 0002-9947 1088-6850 operad, cyclic operad, formality, Kontsevich graph complex, moduli space, Kimura-Stasheff-Voronov operad 21 5 2012 2012-05-21 10.1090/S0002-9947-2012-05553-X http://www.ams.org/journals/tran/2012-364-11/S0002-9947-2012-05553-X/home.html COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2013-06-13T08:36:22.8723663 2012-02-22T13:37:15.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Jeffrey Giansiracusa 0000-0003-4252-0058 1 Paolo Salvatore 2
title Cyclic operad formality for compactified moduli spaces of genus zero surfaces
spellingShingle Cyclic operad formality for compactified moduli spaces of genus zero surfaces
Jeffrey Giansiracusa
title_short Cyclic operad formality for compactified moduli spaces of genus zero surfaces
title_full Cyclic operad formality for compactified moduli spaces of genus zero surfaces
title_fullStr Cyclic operad formality for compactified moduli spaces of genus zero surfaces
title_full_unstemmed Cyclic operad formality for compactified moduli spaces of genus zero surfaces
title_sort Cyclic operad formality for compactified moduli spaces of genus zero surfaces
author_id_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9
author_id_fullname_str_mv 03c4f93e1b94af60eb0c18c892b0c1d9_***_Jeffrey Giansiracusa
author Jeffrey Giansiracusa
author2 Jeffrey Giansiracusa
Paolo Salvatore
format Journal article
container_title Transactions of the American Mathematical Society
container_volume 364
container_issue 11
container_start_page 5881
publishDate 2012
institution Swansea University
issn 0002-9947
1088-6850
doi_str_mv 10.1090/S0002-9947-2012-05553-X
publisher AMS
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.ams.org/journals/tran/2012-364-11/S0002-9947-2012-05553-X/home.html
document_store_str 0
active_str 0
description The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove this we introduce a new complex of graphs in which the differential is a combination of edge deletion and contraction, and we show that this complex resolves BV as a cyclic operad.
published_date 2012-05-21T18:16:49Z
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score 11.1586075

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