Celebratio Mathematica — Chern

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article S. S. Chern and J. White: “Duality properties of characteristic forms,” Invent. Math. 35 : 1 (1976), pp. 285–297. Dedicated to Jean-Pierre Serre. MR 0431193 Zbl 0343.53015

This paper proves various statements and propositions concerning fiber bundles with a Lie group, connections, curvature forms, and characteristic classes, and in particular concerning the recent work of Chern–Simons on secondary characteristic classes [1974] and of Cheeger–Simons on differential characters [1973]. Our main interest in this work is not so much in the characteristic classes but in the differential forms which represent them. Indeed, the aim of this paper is to study the duality properties of the characteristic forms, both the primary ones and the secondary ones. We begin by reviewing some basic notions. For general references, the reader is referred to [Chern 1972; Kobayashi and Nomizu 1963, 1969; Koszul 1973; Milnor and Stasheff 1974].

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