# Modular operads

@article{Getzler1998ModularO, title={Modular operads}, author={Ezra 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…

## 57 Citations

Open-closed modular operads, the Cardy condition and string field theory

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We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its…

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We give a new proof of formality of the operad of little disks. The proof makes use of an operadic version of a simple formality criterion for commutative differential graded algebras due to…

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We give a biased definition of a properad and an explicit example of a closed Frobenius properad. We recall the construction of the cobar complex and algebra over it. We give an equivalent…

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This thesis contains three articles related to operads and moduli spaces of admissible covers of curves. In Paper A we isolate cohomology classes coming from modular forms inside a certain space of…

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Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master…

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