Representatives of the Thom class of a vector bundle

Abstract

After a review of several methods designed to produce equivariant cohomology classes, we apply one introduced by Berline, Getzler and Vergne, to get a family of representatives of the universal Thom class of a vector bundle. Surprisingly, this family does not contain the representative given by Matha\"ı and Quillen. However it contains a particularly simple and symmetric representative that we construct explicitly.