Simplicial currents
type: Item
instance of: scholarly article
title: Simplicial currents
zbMATH Open document ID: 0882.58002
author: Johan L. Dupont
author: Henrik Just
published in: Illinois Journal of Mathematics
publication date: 1998-03-12T00:00:00Z
review text: For a smooth manifold \(X\), the de Rham theorem provides a quasi-isomorphism from the complex \(\Omega^* (X)\) of differential forms into the complex of (smooth) singular cochains on \(M\). This theorem admits an extension to the category of simplicial manifolds, then the complex \(\Omega^* |X|\) of simplicial differential forms undertakes the role of differential forms. The dual version of the de Rham theorem gives a quasi-isomorphism from the complex of (smooth) singular chains on \(X\) to the complex \(\Omega_* (X)\) of compactly supported currents on \(X\). The authors introduce a complex \(\Omega_* |X|\) of the so-called singular currents on a simplicial manifold to obtain the isomorphism \(H(\Omega_* |X|)\to H_* (|X|)\) of the cohomologies of the fat realization \(|X|\) involving the identification of the coalgebra structures.
Mathematics Subject Classification ID: 58A25
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 18F15
Mathematics Subject Classification ID: 57P99
zbMATH DE Number: 1043153
zbMATH Keywords: de Rham theory
zbMATH Keywords: simplicial manifolds
reviewed by: Jan Chrastina
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1043153