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| Format: | Artículo científico |
| Language: | en |
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Academia Brasileira de Ciências
2001
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| Online Access: | https://www.redalyc.org/articulo.oa?id=32773201 |
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| _version_ | 1866815452994338816 |
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| author | Reese Harvey |
| author_facet | Reese Harvey |
| contents | Lefschetz-Pontrjagin Duality for Differential Characters Reese Harvey Blaine Lawson Multidisciplinaria (Ciencias Naturales y Exactas) deRham theory Lefschetz duality Differential characters 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. 2001 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32773201 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.73 |
| format | Artículo científico |
| id | redalyc_32773201 |
| language | en |
| publishDate | 2001 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Lefschetz-Pontrjagin Duality for Differential Characters Reese Harvey Multidisciplinaria (Ciencias Naturales y Exactas) deRham theory Lefschetz duality Differential characters Lefschetz-Pontrjagin Duality for Differential Characters Reese Harvey Blaine Lawson Multidisciplinaria (Ciencias Naturales y Exactas) deRham theory Lefschetz duality Differential characters 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. 2001 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32773201 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.73 |
| title | Lefschetz-Pontrjagin Duality for Differential Characters |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) deRham theory Lefschetz duality Differential characters |
| url | https://www.redalyc.org/articulo.oa?id=32773201 |