Okhezin, V. P. The question of the homotopy invariance of the fixed-point property in the class of compact polyhedra. (Russian) Zbl 0731.55002 Mat. Zametki 46, No. 1, 117-118 (1989). The topological space (X,\({\mathcal T})\) is said to have the fixed-point property if for any continuous mapping \(f:X\to X\) there exists \(x\in X\) such that \(x=f(x)\). It is well-known that the fixed-point property is not invariant under homotopy equivalence in general. The author gives a characterization of invariance of the fixed-point property in the class of compact polyhedra. Reviewer: A.S.Potapov (Voronezh) MSC: 55M20 Fixed points and coincidences in algebraic topology 55M15 Absolute neighborhood retracts PDF BibTeX XML Cite \textit{V. P. Okhezin}, Mat. Zametki 46, No. 1, 117--118 (1989; Zbl 0731.55002)