Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/9169
Title: Moduli spaces and formal operads
Author: Guillén Santos, Francisco
Navarro, Vicenç (Navarro Aznar)
Pascual, Pere (Pascual i Gainza)
Roig Martí, Agustí
Keywords: Mòduls (Àlgebra)
Àlgebra homològica
Categories (Matemàtica)
Families, algebraic moduli (curves)
Operads
Nonabelian homotopical algebra
Issue Date: 2005
Publisher: Duke University Press
Abstract: Let 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.
Note: Reproducció del document publicat a http://dx.doi.org/10.1215/S0012-7094-05-12924-6
It is part of: Duke Mathematical Journal, 2005, vol. 129, núm. 2, p. 291-335.
Related resource: http://dx.doi.org/10.1215/S0012-7094-05-12924-6
URI: http://hdl.handle.net/2445/9169
ISSN: 0012-7094
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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