On the de Rham complex in abstract spaces
type: Item
instance of: scholarly article
title: On the de Rham complex in abstract spaces
zbMATH Open document ID: 0933.55019
DOI: 10.1007/BF02169287
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-01-25T00:00:00Z
review text: It is well understood that the exactness of the de Rham complex (firstly obtained for finite-dimensional manifolds and next extended to Banach manifolds, Fréchet manifolds, locally convex spaces) is of great importance because it describes the singular cohomology. The aim of this paper is to give conditions under which a de Rham complex is constructed and is exact, within the framework of abstract sheaves of differentiable functions taking values in an arbitrary topological algebra \({\mathcal A}\) instead of the field \(\mathbb{R}\) of real numbers.
Mathematics Subject Classification ID: 55U05
Mathematics Subject Classification ID: 18F99
Mathematics Subject Classification ID: 57N25
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 55N99
zbMATH DE Number: 1393018
zbMATH Keywords: differential triad of an algebra
zbMATH Keywords: de Rham complex of a module
zbMATH Keywords: sheaf of algebras
author: M. H. Papatriantafillou
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1393018