2008/08/04 by Hanno von Bodecker, von Bodecker, Hanno
Mathematics · #55Q45 #58J26 #58J28 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:55Q45 #msc:58J26 #msc:58J28
paper · pdf · doi:10.48550/arxiv.0808.0428
67 pages; updated Lemma D.4 and subsequent calculation
openalex publication_date 2008/08/04 · arxiv created 2009/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.