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Chern-simons forms on associated bundles, and boundary terms

David L. Johnson
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Abstract

Let $E$ be a principle bundle over a compact manifold $M$ with compact structural group $G$. For any $G$-invariant polynomial $P$, The transgressive forms $TP(ω)$ defined by Chern and Simons are shown to extend to forms $ΦP(ω)$ on associated bundles $B$ with fiber a quotient $F=G/H$ of the group. These forms satisfy a heterotic formula $$dΦP(ω)=P(Ω)-P(Ψ),$$ relating the characteristic form $P(Ω)$ to a fiber-curvature characteristic form. For certain natural bundles $B$, $P(Ψ)=0$, giving a true transgressive form on the associated bundle, which leads to the standard obstruction properties of characteristic classes as well as natural expressions for boundary terms.

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David L. Johnson. 2006-01-09. Chern-simons forms on associated bundles, and boundary terms. https://arxiv.org/abs/math/0601182

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