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.

Giansiracusa, J., Salvatore, P. (2012). Cyclic operad formality for compactified moduli spaces of genus zero surfaces. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364(11), 5881-5911 [10.1090/S0002-9947-2012-05553-X].

Cyclic operad formality for compactified moduli spaces of genus zero surfaces

SALVATORE, PAOLO
2012-01-01

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.
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Giansiracusa, J., Salvatore, P. (2012). Cyclic operad formality for compactified moduli spaces of genus zero surfaces. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364(11), 5881-5911 [10.1090/S0002-9947-2012-05553-X].
Giansiracusa, J; Salvatore, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/90011
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