Modular operads

@article{Getzler1998ModularO,
  title={Modular operads},
  author={E. Getzler and M. M. Kapranov},
  journal={Compositio Mathematica},
  year={1998},
  volume={110},
  pages={65-125}
}
We develop a ‘higher genus’ analogue of operads, which we call modular operads, in which graphs replace trees in the definition. We study a functor F on the category of modular operads, the Feynman transform, which generalizes Kontsevich’s graph complexes and also the bar construction for operads. We calculate the Euler characteristic of the Feynman transform, using the theory of symmetric functions: our formula is modelled on Wick’s theorem. We give applications to the theory of moduli spaces… Expand
Open-closed modular operads, Cardy condition and string field theory
Topology of moduli spaces and operads
Operadic categories and Duoidal Deligne's conjecture
Properads and Homotopy Algebras Related to Surfaces
Moduli spaces of Klein surfaces and related operads
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