On the geometry of the f-invariant

Abstract

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.

67 pages; updated Lemma D.4 and subsequent calculation

Cited by in corpus (5)

• beta-family congruences and the f-invariant
• The universal eta-invariant for manifolds with boundary
• Toda brackets and congruences of modular forms
• An analytical formula for the f-invariant of circle transfers
• Twisted Dirac operators on certain nilmanifolds associated to even lattices