The A-infinity operad and the moduli space of curves

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.

14 pages. Version 2: references added, proofs cleaned up

References in corpus (6)

• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• Tessellations of Moduli Spaces and the Mosaic Operad
• Some Comments on Branes, G-flux, and K-theory
• Arc Operads and Arc Algebras
• Infinity-Inner-Products on A-Infinity-Algebras
• Homotopy Inner Products for Cyclic Operads

Cited by in corpus (8)

• Crossed simplicial groups and structured surfaces
• Moduli spaces of Klein surfaces and related operads
• Kontsevich's Swiss Cheese Conjecture
• The A-infinity Deformation Theory of a Point and the Derived Categories of Local Calabi-Yaus
• Operads and moduli spaces
• Regular patterns, substitudes, Feynman categories and operads
• The modular envelope of the cyclic operad Ass
• Non-commutative moduli spaces of topological D-branes