Show simple item record

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.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.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshCategories (Mathematics)
dc.subject.otherModuli spaces
dc.subject.otherformal operads
dc.titleModuli spaces and formal operads
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

Files in this item


This item appears in the following Collection(s)

Show simple item record

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