Equivariant Chern Character for the Invariant Dirac Operator

摘要

The attributes of elliptic pseudodifferential systems that have relevance within Atiyah-Singer index theory have been abstracted to the concept of Fredholm modules, or K-cycles in the language of K-homology. Pairing of a K-cycle with a K-cocycle gives the index. Connes invented cyclic cohomology while looking for a homology-cohomology formula of this pairing. The Chern-Connes character relates finitely summable Fredholm modules to cyclic cocycles and, more generally, relates Θ-summable Fredholm modules to entire cyclic cocycles. We refer to [5], and to [4] for the background and definitions.