The longitudinal index theorem for foliations (original) (raw)

This paper establishes a K-theoretical version of the index theorem specifically for longitudinal elliptic differential operators in the context of foliations, leveraging the framework of bivariant K-theory developed by Kasparov. The theorem generalizes existing results for cases where foliations are defined by fibration fibers and accommodates arbitrary foliations, not limited by the presence of holonomy invariant transverse measures. The core finding equates the analytic index of an elliptic operator to a topological index within the bivariant K-theory framework.