Asian Journal of Mathematics

Harmonic forms on principal bundles

Corbett Redden

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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.

Article information

Asian J. Math., Volume 16, Number 4 (2012), 637-660.

First available in Project Euclid: 12 December 2012

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Primary: 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]
Secondary: 58J28: Eta-invariants, Chern-Simons invariants 55T10: Serre spectral sequences

Hodge theory adiabatic limit Chern–Simons forms Serre spectral sequence


Redden, Corbett. Harmonic forms on principal bundles. Asian J. Math. 16 (2012), no. 4, 637--660.

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