Differential characters and geometric invariants. (English) Zbl 0621.57010

Geometry and topology, Proc. Spec. Year, College Park/Md. 1983/84, Lect. Notes Math. 1167, 50-80 (1985).
[For the entire collection see Zbl 0568.00014.]
From the summary: ”This paper first appeared in a collection of lecture notes which were distributed at the AMS Summer Institute of Differential Geometry, held at Stanford in 1973. We sketch the study of a functor which assigns to a smooth manifold M a certain graded ring \(\hat H^*(M)\), the ring of differential characters on M. Perhaps the main interest of our construction comes from the fact that the Weil homomorphism can be naturally factored through \(\hat H^*\). We should mention that our invariants are closely related to the differential forms TP(\(\theta)\) on the total space of a principal bundle with connection. These were considered by S. Chern and the second author [Ann. Math., II. Ser. 99, 48-69 (1974; Zbl 0283.53036)].
In fact, the present work arose out of the attempt to define objects in the base playing a role analogous to that of TP(\(\theta)\). Earlier results in this direction were formulated by the second author [”Characteristic forms and transgressions. II: Characters associated to a connection” (preprint)].”
Reviewer: P.Walczak


57R20 Characteristic classes and numbers in differential topology
53C40 Global submanifolds
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
53C20 Global Riemannian geometry, including pinching
58A12 de Rham theory in global analysis
55R10 Fiber bundles in algebraic topology