Homotopy dominations within polyhedra

Tom 178 / 2003

Danuta Kołodziejczyk 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
    Polish Academy of Sciences
    /Sniadeckich 8
    00-956 Warszawa, Poland
    e-mail

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