Moduli Spaces and Formal Operads
| dc.creator | Guillen, F. | |
| dc.creator | Navarro, V. | |
| dc.creator | Pascual, P. | |
| dc.creator | Roig, A. | |
| dc.date | 2004-02-06 | |
| dc.date | 2004-03-01 | |
| dc.date.accessioned | 2026-07-07T06:24:43Z | |
| dc.date.available | 2026-07-07T06:24:43Z | |
| dc.description | 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. | |
| dc.description | 36 pages (v3: some typographical corrections) | |
| dc.identifier | https://arxiv.org/abs/math/0402098 | |
| dc.identifier | http://arxiv.org/abs/math/0402098 | |
| dc.identifier | Duke Math. J., vol 129, N0. 2, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96639 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14FXX; 55XX | |
| dc.title | Moduli Spaces and Formal Operads | |
| dc.type | text |