# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Homotopy dominations within polyhedra

### Tom 178 / 2003

Fundamenta Mathematicae 178 (2003), 189-202 MSC: 55P55, 55P15. DOI: 10.4064/fm178-3-1

#### Streszczenie

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, $\pi _1(P)$ may be any given non-abelian poly-${{\mathbb Z}}$-group and $\mathop {\rm dim}\nolimits P$ may be any given integer $n \geq 3$.

#### Autorzy

• Danuta KołodziejczykFaculty of Mathematics and Informational Sciences
Warsaw University of Technology
Pl. Politechniki 1
00-661 Warszawa, Poland
and
Institute of Mathematics