Cyclic operad formality for compactified moduli spaces of genus zero surfaces

Giansiracusa, Jeffrey; Salvatore, Paolo

doi:10.1090/S0002-9947-2012-05553-X

Cyclic operad formality for compactified moduli spaces of genus zero surfaces

Authors: Jeffrey Giansiracusa and Paolo Salvatore
Journal: Trans. Amer. Math. Soc. 364 (2012), 5881-5911
MSC (2010): Primary 18D50; Secondary 55P48, 14H15, 81Q30, 81T45
DOI: https://doi.org/10.1090/S0002-9947-2012-05553-X
Published electronically: May 21, 2012
MathSciNet review: 2946936
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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.

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