Lefschetz-Pontrjagin duality for differential characters

• Autor(a) principal: HARVEY,REESE
• Data de Publicação: 2001
• Outros Autores: LAWSON,BLAINE
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Anais da Academia Brasileira de Ciências (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200001
• topic: Differential characters; Lefschetz duality; deRham theory

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 <img src="http:/img/fbpe/aabc/v73n2/fo1.gif" alt="fo1.gif (867 bytes)"> given by (alpha, beta) <img SRC="http:/img/fbpe/aabc/v73n2/m1img7.gif"> (alpha * beta) [X] induces isomorphisms <img src="http:/img/fbpe/aabc/v73n2/fo2.gif" alt="fo2.gif (1110 bytes)"> <img src="http:/img/fbpe/aabc/v73n2/fo3.gif" alt="fo3.gif (1086 bytes)"> onto the smooth Pontrjagin duals. In particular, <img SRC="http:/img/fbpe/aabc/v73n2/m1img13.gif"> and <img SRC="http:/img/fbpe/aabc/v73n2/m1img13a.gif"> 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, <img SRC="http:/img/fbpe/aabc/v73n2/m1img14.gif">X). The relation of the sequence to the duality mappings is analyzed.