Homotopy dominations within polyhedra
Fundamenta Mathematicae, Tome 178 (2003) no. 3, p. 189.

Voir la notice de l'article dans European Digital Mathematics Library

We show the existence of a finite polyhedron P dominating infinitely many different homotopy types of finite polyhedra and such that there is a bound on the lengths of all strictly descending sequences of homotopy types dominated by P. This answers a question of K. Borsuk (1979) dealing with shape-theoretic notions of "capacity" and "depth" of compact metric spaces. Moreover, π₁(P) may be any given non-abelian poly-ℤ-group and dim P may be any given integer n ≥ 3.
Classification : 55P15, 55P55
Mots-clés : shape or homotopy domination, compactum, polyhedron, capacity, depth 
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Danuta Kołodziejczyk. Homotopy dominations within polyhedra. Fundamenta Mathematicae, Tome 178 (2003) no. 3, p. 189. https://geodesic-test.mathdoc.fr/item/FUNDAM_2003__178_3_283186/