Modular operads

E. Getzler*, M. M. Kapranov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

137 Scopus citations


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 of pointed algebraic curves.

Original languageEnglish (US)
Pages (from-to)65-125
Number of pages61
JournalCompositio Mathematica
Issue number1
StatePublished - 1998


  • Bar-construction
  • Feynman diagram
  • Graph
  • Operad
  • Symmetric functions

ASJC Scopus subject areas

  • Algebra and Number Theory


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