Moduli Spaces and Formal Operads

Details Moduli Spaces and Formal Operads Moduli Spaces and Formal Operads

2004-02-06

arxiv.org/abs/math/0402098v3

Duke Math. J., vol 129, N0. 2, 2005

Mathematics

Algebraic Geometry

36 pages (v3: some typographical corrections)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Moduli Spaces and Formal Operads does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Moduli Spaces and Formal Operads, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Moduli Spaces and Formal Operads will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-657029