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From sparks to grundles – differential characters. (English) Zbl 1116.53048
Summary: We introduce a new homological machine for the study of secondary geometric invariants. The objects, called spark complexes, occur in many areas of mathematics. The theory is applied here to establish the equivalence of a large family of spark complexes which appear naturally in geometry, topology and physics. These complexes are quite different. Some of them are purely analytic, some are simplicial, some are of Čech-type, and many are mixtures. However, the associated theories of secondary invariants are all shown to be canonically isomorphic. Numerous applications and examples are explored.

MSC:
53C65 Integral geometry
58A25 Currents in global analysis
57R19 Algebraic topology on manifolds and differential topology
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