Bouquets revisited and equivariant elliptic cohomology

Abstract

Let [Formula: see text] be an even-dimensional spin manifold with action of a compact Lie group [Formula: see text]. We review the construction of bouquets of analytic equivariant cohomology classes and of [Formula: see text]-integration. Given an elliptic curve [Formula: see text], we introduce, as in Grojnowski, elliptic bouquets of germs of holomorphic equivariant cohomology classes on [Formula: see text]. Following Bott–Taubes and Rosu, we show that integration of an elliptic bouquet is well defined. In particular, this imply Witten’s rigidity theorem. Our systematic use of the Chern–Weil construction of equivariant classes allows us to reduce proofs to algebraic identities.