The A-infinity operad and the moduli space of curves
Algebraic Geometry
2007-05-23 v2 Quantum Algebra
Abstract
The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the A-infinity cyclic operad. This gives a new proof of the result of Harer-Mumford-Thurston-Penner-Kontsevich that a cell complex built from ribbon graphs is homotopy equivalent to the moduli space of curves.
Keywords
Cite
@article{arxiv.math/0402015,
title = {The A-infinity operad and the moduli space of curves},
author = {Kevin Costello},
journal= {arXiv preprint arXiv:math/0402015},
year = {2007}
}
Comments
14 pages. Version 2: references added, proofs cleaned up