Formal differential graded algebras and homomorphisms
type: Item
instance of: scholarly article
title: Formal differential graded algebras and homomorphisms
zbMATH Open document ID: 0644.55010
DOI: 10.1016/0022-4049(88)90076-X
author: Martin Arkowitz
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: The Sullivan theory of rational homotopy associates to each topological space X a minimal model \(M_ X\). This is a commutative differential graded algebra over the field \({\mathbb{Q}}\) which describes completely the rational homotopy type of the space X. When there is a weak equivalence, in the category of C.D.G.A., between \(M_ X\) and \(H^*(X;{\mathbb{Q}})\) the space X is called formal. In the same way, one can define a formal map between two formal spaces. The main result of this paper states: if X and Y are both formal spaces then the natural function: \([X,Y]\to Hom(H^*(Y;{\mathbb{Q}}),H^*(X;{\mathbb{Q}}))\) restricted to the homotopy classes of formal maps is a bijection. This theorem has several consequences including results on the group of self-equivalences of a formal space.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P10
zbMATH DE Number: 4050543
zbMATH Keywords: formal spaces
zbMATH Keywords: homotopy classes of formal maps
zbMATH Keywords: group of self- equivalences of a formal space
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4050543