Cyclic operad formality for compactified moduli spaces of genus zero surfaces

Details Cyclic operad formality for compactified moduli spaces of genus zero surfaces Cyclic operad formality for compactified moduli spaces of genus zero surfaces

2009-11-23

arxiv.org/abs/0911.4430v2

Mathematics

Quantum Algebra

30 pages. A new title and some changes in the exposition have been introduced

Scientific paper

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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