The S 1 -Equivariant Cohomology of Homogeneous Spaces as Deformations of Algebras

Abstract

Let G be a compact connected Lie group and K a maximal rank subgroup of G. The homogeneous space G/K has the S1-action defined by left translations induced from a homomorphism from S1 to G. In this paper, we study a problem on the realization of some deformation of the cohomology algebra H*(G/K; Fp) by the S1-equivariant cohomology of G/K. In consequence, for the case where G is a classical Lie group, it follows that there exists at most one essentially different homomorphism from S1 to G which realizes a given deformation, and that the homomorphism is controlled by an appropriate equation in one indeterminate.