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Title: | Moduli spaces and formal operads |
Author: | Guillén Santos, Francisco Navarro, Vicenç (Navarro Aznar) Pascual Gainza, Pere Roig, 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. |
URI: | http://hdl.handle.net/2445/9169 |
Related resource: | http://dx.doi.org/10.1215/S0012-7094-05-12924-6 |
ISSN: | 0012-7094 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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