From Sparks to Grundles--Differential Characters
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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 Cech-type, and many are mixtures. However, the associated theories of secondary invariants are all shown to be canonically isomorphic. We also show that Differential characters factor to a much smaller, more geometric group, the set of holonomy maps. Numerous applications and examples are explored.
25 pages, An extensive section on applications and examples has been added. Abstract: We introduce a new homological machine for the study of secondary geometric invariants. The objects are called spark complexes. 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. However, the associated theories of secondary invariants are all shown to be canonically isomorphic
25 pages, An extensive section on applications and examples has been added. Abstract: We introduce a new homological machine for the study of secondary geometric invariants. The objects are called spark complexes. 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. However, the associated theories of secondary invariants are all shown to be canonically isomorphic