Moduli Spaces and Formal Operads

dc.creatorGuillen, F.
dc.creatorNavarro, V.
dc.creatorPascual, P.
dc.creatorRoig, A.
dc.date2004-02-06
dc.date2004-03-01
dc.date.accessioned2026-07-07T06:24:43Z
dc.date.available2026-07-07T06:24:43Z
dc.descriptionLet 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.
dc.description36 pages (v3: some typographical corrections)
dc.identifierhttps://arxiv.org/abs/math/0402098
dc.identifierhttp://arxiv.org/abs/math/0402098
dc.identifierDuke Math. J., vol 129, N0. 2, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96639
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subjectQuantum Algebra
dc.subject14FXX; 55XX
dc.titleModuli Spaces and Formal Operads
dc.typetext

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