The homotopy types of retracts of a fixed space
type: Item
instance of: scholarly article
title: The homotopy types of retracts of a fixed space
zbMATH Open document ID: 0724.55010
DOI: 10.1016/0022-4049(91)90024-V
author: Lex E. Renner
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author proves that if X is a simply connected CW complex such that \(H^*(X;{\mathbb{Q}})\) is finitely generated as an algebra then there are only finitely many rational homotopy types among the retracts of X. The proof is based on the study of the properties of homotopy idempotents and a finiteness property of linear semigroups.
Mathematics Subject Classification ID: 55P62
zbMATH DE Number: 4194704
zbMATH Keywords: CW complex
zbMATH Keywords: rational homotopy types
zbMATH Keywords: retracts
zbMATH Keywords: homotopy idempotents
zbMATH Keywords: linear semigroups
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
cites work: Cohomology theories
cites work: Uniqueness of Product and Coproduct Decompositions in Rational Homotopy Theory
cites work: On Linear Algebraic Semigroups
cites work: Q4040248
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description: scientific article; zbMATH DE number 4194704