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The framed little 2-discs operad is homotopy equivalent to theKimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stablecurves with tangent rays at the marked points and nodes. We show that thiscyclic operad is formal, meaning that its chains and its homology (theBatalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove thiswe introduce a new complex of graphs in which the differential is a combinationof edge deletion and contraction, and we show that this complex resolves BV asa cyclic operad.

Cyclic operad formality for compactified moduli spaces of genus zero surfaces