15 August 2005 Moduli spaces and formal operads
V. Navarro, P. Pascual, A. Roig, F. Guillén Santos
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Duke Math. J. 129(2): 291-335 (15 August 2005). DOI: 10.1215/S0012-7094-05-12924-6


Let M̲g,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations that relate the different moduli spaces identifying marked points, the family (M̲g,l)g,l is a modular operad of projective smooth Deligne-Mumford stacks M̲. In this paper, we prove that the modular operad of singular chains S*(M̲;Q) is formal, so it is weakly equivalent to the modular operad of its homology H*(M̲;Q). As a consequence, the up-to-homotopy algebras of these two operads are the same. To obtain this result, we prove a formality theorem for operads analogous to the Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field.


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V. Navarro. P. Pascual. A. Roig. F. Guillén Santos. "Moduli spaces and formal operads." Duke Math. J. 129 (2) 291 - 335, 15 August 2005. https://doi.org/10.1215/S0012-7094-05-12924-6


Published: 15 August 2005
First available in Project Euclid: 27 September 2005

zbMATH: 1120.14018
MathSciNet: MR2165544
Digital Object Identifier: 10.1215/S0012-7094-05-12924-6

Primary: 14H10 , 18D50

Rights: Copyright © 2005 Duke University Press


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Vol.129 • No. 2 • 15 August 2005
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