The Transfer and Compact Lie Groups

Abstract

Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be l-universal classifying spaces, with $\rho (H,G):BH \to BG$ the natural projection. Then transfer homomorphisms $T(H,G):h(BH) \to h(BG)$ are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset theorem in the above more general context, expressing ${\rho ^{\ast }}(K,G) \circ T(H,G)$ as a sum of other compositions. The main theorems were announced in the Bulletin of the American Mathematical Society in May 1977.