Lefschetz-Pontrjagin duality for differential characters

Anais da Academia Brasileira de Ciências

Reese Harvey²  Blaine Lawson¹ 

[1] ,Rice University The Department of Mathematics Houston TX

关键词: Differential characters;    Lefschetz duality;    deRham theory;    caracteres diferenciais;    dualidade de Lefschetz;    teoria de deRham;   

DOI  :  10.1590/S0001-37652001000200001

来源: SciELO

【 摘 要 】

A theory of differential 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 given by (alpha, beta) (alpha * beta) [X] induces isomorphisms onto the smooth Pontrjagin duals. In particular, and 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.

【 授权许可】

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