Lefschetz-Pontrjagin Duality for Differential Characters - Reese Harvey (Anais da Academia Brasileira de Ciências, 2001)
A theory of differential characters is developed for manifolds with boundary. This is done fromboth the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paperis the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that thepairingHk(X, ∂X) × Hn−k−1(X) −→ S1given by (α, β) → (α * β) [X] induces isomorphismsD : Hk(X, ∂X) → Hom∞(Hn−k−1(X), S1)D : Hn−k−1(X) → Hom∞(Hk(X, ∂X), S1)onto the smooth Pontrjagin duals. In particular, D and D are injective with dense range in thegroup of all continuous homomorphisms into the circle. A coboundary map is introduced whichyields a long sequence for the character groups associated to the pair (X, ∂X). The relation of thesequence to the duality mappings is analyzed.