Harmonic forms on principal bundles

2008/10/25 by Corbett Redden, Redden, Corbett
Mathematics · #58A14 #58J28 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58A14 #msc:58J28

paper · pdf · doi:10.48550/arxiv.0810.4578

26 pages; v2 corrected typos and minor revisions

arxiv created 2010/01/06 · arxiv updated 2010/01/07

Abstract

We show a relationship between Chern-Simons 1- and 3-forms and harmonic forms on a principal bundle. Doing so requires one to consider an adiabatic limit. For the 3-form case, assume that G is simple and the corresponding Chern-Weil 4-form is exact. Then, the Chern-Simons 3-form on the princpal bundle G-bundle, minus a canonical term from the base, is harmonic in the adiabatic limit.

Related

• Intrinsically harmonic forms and characterization of flat circle bundles
• Chern-simons forms on associated bundles, and boundary terms
• Flat extensions of principal connections and the Chern-Simons 3-form
• Elliptic Genera, Transgression and Loop Space Chern-Simons Forms
• Bott-Chern and ∂ Harmonic forms on Almost Hermitian 4-manifolds