Equivariant Formal Group Laws

Abstract

Motivated by complex oriented equivariant cohomology theories, we give a natural algebraic definition of an $A$-equivariant formal group law for any abelian compact Lie group $A$. The complex oriented cohomology of the classifying space for line bundles gives an example. We also show how the choice of a complete flag gives rise to a basis and a means of calculation. This allows us to deduce that there is a universal ring $L_A$ for $A$-equivariant formal group laws and that it is generated by the Euler classes and the coefficients of the coproduct of the orientation. We study a number of topological cases in some detail. 1991 Mathematics Subject Classification: 14L05, 55N22, 55N91, 57R85.