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dc.contributor.authorGuillén Santos, Francisco
dc.contributor.authorNavarro, Vicenç (Navarro Aznar)
dc.contributor.authorPascual Gainza, Pere
dc.contributor.authorRoig Martí, Agustín
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2007-05-07T15:38:03Z
dc.date.available2007-05-07T15:38:03Z
dc.date.created2003
dc.date.issued2003
dc.identifier.urihttp://hdl.handle.net/2117/906
dc.description.abstractLet Mg,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations which relate the different moduli spaces identifying marked points, the family (Mg,l)g,l is a modular operad of projective smooth Deligne-Mumford stacks, M. In this paper we prove that the modular operad of singular chains C?(M;Q) is formal; so it is weakly equivalent to the modular operad of its homology H?(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-Grifiths-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.
dc.format.extent36
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.subject.lcshCurves
dc.subject.lcshCategories (Mathematics)
dc.subject.otherModuli spaces
dc.subject.otherformal operads
dc.titleModuli spaces and formal operads
dc.typeArticle
dc.subject.lemacCorbes
dc.subject.lemacCategories (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.subject.amsClassificació AMS::14 Algebraic geometry::14H Curves
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18D Categories with structure
dc.rights.accessOpen Access


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Except where otherwise noted, content on this work is licensed under a Creative Commons license: Attribution-NonCommercial-NoDerivs 2.5 Spain