Abstract
61. THE MAIN RESULTS THE PURPOSE of this note is to show that the differential characters associated to a compact Lie group G (as defined by Chern, Simons and Cheeger) comprise its Bore1 cohomology H&,,(G,R/Z). Along the way we obtain some interesting formulae for these characters as cochains in the bar resolution for G, and obtain some results on the cohomology of certain bundles with discrete structure group. Let % be the Lie algebra of G and let I(%, R) be the ring of Weil polynomials, i.e. symmetric multilinear functions on Yl which are invariant under the Adjoint action of G. In 121 Chern and Simons showed how to use a connection 8 on a principal G-bundle E-B to determine a characteristic form TP(8) in A*(E, R) for every P E I(%, R). These forms satisfy the equation
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