Formality in an Equivariant Setting

Abstract

We define and discuss G-formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over R, where R is the cohomology of the classifying space BG. These results may be applied in computing the equivariant cohomology of their loop spaces.