Lefschetz-Pontrjagin duality for differential characters
type: Item
instance of: scholarly article
title: Lefschetz-Pontrjagin duality for differential characters
zbMATH Open document ID: 0992.32003
DOI: 10.1590/S0001-37652001000200001
author: F. Reese Harvey
author: H. Blaine jun. Lawson
published in: Anais da Academia Brasileira de Ciências
publication date: 2002-09-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0512528
Mathematics Subject Classification ID: 32C30
Mathematics Subject Classification ID: 58A25
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1626443
zbMATH Keywords: Lefschetz-Pontryagin duality
zbMATH Keywords: differential characters
MaRDI profile type: Publication
arXiv ID: math/0512528
cites work: Q4772354
cites work: Q5849999
cites work: Q4273951
cites work: Geometric Residue Theorems
OpenAlex ID: W2167390716
review text: An analog of the Lefschetz-Pontryagin Duality Theorem for differential characters for compact manifolds with boundary \((X,\partial X)\) is presented. One asserts the existence of a pairing NEWLINE\[NEWLINE\widehat {\mathbb{H}}^k(X) \times \widehat {\mathbb{H}}^{n-k-1} (X,\partial X)\to S^1NEWLINE\]NEWLINE given by \((\alpha,\beta) \mapsto (\alpha* \beta)[X]\) and inducing injective maps with dense range. Coboundary maps \(\partial:\widehat {\mathbb{H}}^k(X) \to\widehat {\mathbb{H}}^{k+1} (X, \partial X)\) intertwine the duality mappings and reduce the standard picture under the natural transformation to integral cohomology.NEWLINENEWLINENEWLINESee also \textit{F. R. Harvey} and \textit{H. B. Lawson jun.}, `A theory of characteristic currents associated with a singular connection', Astérisque 213 (1993; Zbl 0804.53037) and Am. J. Math. 117, 829-873 (1995; Zbl 0851.58036).
reviewed by: Maido Rahula
description: scientific article; zbMATH DE number 1626443