The f-invariant and index theory
  In this paper we prove a tertiary index theorem which relates a spectral geometric and a homotopy theoretic invariant of an almost complex manifold with framed boundary. It is derived from the index theoretic and homotopy theoretic versions of a complex elliptic genus and interestingly related with the structure of the stable homotopy groups of spheres. 
Ulrich Bunke and Niko Naumann