Asian Journal of Mathematics

Volume 16 (2012)

Number 4

Harmonic forms on principal bundles

Pages: 637 – 660

DOI: https://dx.doi.org/10.4310/AJM.2012.v16.n4.a4

Author

Corbett Redden (Department of Mathematics, Long Island University, Brookville, New York)

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.

Keywords

Hodge theory, adiabatic limit, Chern–Simons forms, Serre spectral sequence

2010 Mathematics Subject Classification

Primary 58A14. Secondary 55T10, 58J28.

Published 10 December 2012