Guillén Santos, FranciscoNavarro, Vicenç (Navarro Aznar)Pascual Gainza, PereRoig, Agustí2009-08-192009-08-1920050012-7094https://hdl.handle.net/2445/9169Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};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 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.45 p.application/pdfeng(c) Duke University Press, 2005Mòduls (Àlgebra)Àlgebra homològicaCategories (Matemàtica)Families, algebraic moduli (curves)OperadsNonabelian homotopical algebrainfo:eu-repo/semantics/article519204info:eu-repo/semantics/openAccess