Lefschetz-Pontrjagin Duality for Differential Characters
نویسنده
چکیده
A theory of di erential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing c IHk(X; @X) c IHn k 1(X) ! S1 given by ( ; ) 7! ( ) [X] induces isomorphisms D : c IHk(X; @X)! Hom1(c IHn k 1(X); S1) D0 : c IHn k 1(X)! Hom1(c IHk(X; @X); S1) onto the smooth Pontrjagin duals. In particular, D and D0 are injective with dense range in the group of all continuous homomorphisms into the circle. A coboundary map is introduced which yields a long sequence for the character groups associated to the pair (X; @X). The relation of the sequence to the duality mappings is analyzed.
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