Harmonic forms on principal bundles

Details Harmonic forms on principal bundles Harmonic forms on principal bundles

2008-10-25

arxiv.org/abs/0810.4578v2

Mathematics

Differential Geometry

26 pages; v2 corrected typos and minor revisions

Scientific paper

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.

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