Topological Aspects of Differential Chains
Identifieur interne : 000245 ( Main/Curation ); précédent : 000244; suivant : 000246Topological Aspects of Differential Chains
Auteurs : J. Harrison [États-Unis] ; H. Pugh [Royaume-Uni]Source :
- Journal of Geometric Analysis [ 1050-6926 ] ; 2012-07-01.
English descriptors
Abstract
Abstract: In this paper we investigate the topological properties of the space of differential chains $\,^{\prime}\mathcal{B}(U)$ defined on an open subset U of a Riemannian manifold M. We show that $\,^{\prime}\mathcal {B}(U)$ is not generally reflexive, identifying a fundamental difference between currents and differential chains. We also give several new brief (though non-constructive) definitions of the space $\,^{\prime}\mathcal{B}(U) $ , and prove that it is a separable ultrabornological (DF)-space. Differential chains are closed under dual versions of the fundamental operators of the Cartan calculus on differential forms (Harrison in Geometric Poincare lemma, Jan 2011, submitted; Operator calculus—the exterior differential complex, Jan 2011, submitted). The space has good properties, some of which are not exhibited by currents $\mathcal{B}'(U)$ or $\mathcal{D}'(U)$ . For example, chains supported in finitely many points are dense in $\,^{\prime}\mathcal{B}(U)$ for all open U⊂M, but not generally in the strong dual topology of $\mathcal{B}'(U)$ .
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DOI: 10.1007/s12220-010-9210-8
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