Modular operads

E. Getzler*, M. M. Kapranov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

116 Scopus citations

Abstract

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
Volume110
Issue number1
DOIs
StatePublished - 1998

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Modular operads'. Together they form a unique fingerprint.

Cite this