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

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- by Jeffrey Giansiracusa and Paolo Salvatore PDF
- Trans. Amer. Math. Soc.
**364**(2012), 5881-5911 Request permission

## 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.## References

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## Additional Information

**Jeffrey Giansiracusa**- Affiliation: Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom
- Email: j.h.giansiracusa@gmail.com
**Paolo Salvatore**- Affiliation: Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
- Email: salvator@mat.uniroma2.it
- Received by editor(s): September 10, 2010
- Received by editor(s) in revised form: January 25, 2011
- Published electronically: May 21, 2012
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2946936