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Cyclic operad formality for compactified moduli spaces of genus zero surfaces / Jeffrey Giansiracusa; Paolo Salvatore

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

Swansea University Author: Giansiracusa, Jeffrey

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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
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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-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.
Keywords: operad, cyclic operad, formality, Kontsevich graph complex, moduli space, Kimura-Stasheff-Voronov operad
College: College of Science
Issue: 11
Start Page: 5881
End Page: 5911