2006/01/09 by David L. Johnson, Johnson, David L.
Mathematics · #53C05 #57R20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C05 #msc:57R20
paper · pdf · doi:10.48550/arxiv.math/0601182
15 pages, no figures, AMS-LaTeX
arxiv created 2006/01/09 · openalex publication_date 2006/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.