Equivariant cyclic homology and equivariant differential forms

Abstract

Let G be a compact Lie group, and let M be a compact manifold on which G acts smoothly. In this paper, we give a description of the equivariant periodic cyclic homology HP^ (C°° (M)) of C°° (M) as the cohomology of global equivariant differential forms on M: these are sections of a sheaf over the group G, whose stalk at g (E G is the complex of equivariant differential forms on the fixed-point set M 8 , with action of the centralizer 0 s .