  The f-invariant is a higher version of the e-invariant that takes values in
the divided congruences between modular forms; it can be formulated as an
elliptic genus of manifolds with corners of codimension two.
  In this thesis, we develop a geometrical interpretation of the f-invariant in
terms of index theory, thereby providing an analytical link between the stable
homotopy groups of the spheres and the arithmetic of modular forms. In
particular, we are able to establish a formula that allows us to compute the
f-invariant from a single face. Furthermore, we apply our results to the
situation of cartesian products and principal circle bundles, performing
explicit calculations.
