FORMAL GROUPS AND THE ATIYAH-HIRZEBRUCH FORMULA

Abstract

In this article, manifolds with actions of compact Lie groups are considered. For each rational Hirzebruch genus , an equivariant genus , a homomorphism from the bordism ring of -manifolds to the ring , is constructed. With the aid of the language of formal groups, for some genera it is proved that for a connected compact Lie group , the image of belongs to the subring . As a consequence, extremely simple relations between the values of these genera on bordism classes of -manifolds and submanifolds of its fixed points are found. In particular, a new proof of the Atiyah-Hirzebruch formula is obtained.Bibliography: 10 items.