Asian Journal of Mathematics

Volume 16 (2012)

Number 4

Harmonic forms on principal bundles

Pages: 637 – 660

DOI: http://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.

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