Ezra Getzler

Modular operads revisited.


Modular operads were introduced, in joint work with Kapranov, for two reasons: to understand the axiomatization of quantum field theory in two dimensions, and to give a natural setting for Kontsevich's graph complexes. In this talk, I show how to incorporate an open sector into the definition of modular operads. At the same time, I present a new point of view on modular operads, in which the role of representations of the symmetric group Sn is taken by representations of the mapping class groups for surfaces with boundary.