On the geometry of the f-invariant

Details On the geometry of the f-invariant On the geometry of the f-invariant

2008-08-04

arxiv.org/abs/0808.0428v2

Mathematics

Differential Geometry

67 pages; updated Lemma D.4 and subsequent calculation

Scientific paper

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.

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