The homotopy types of retracts of a fixed space
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.
scientific article; zbMATH DE number 4194704
scientific article