Polyhedra with finite fundamental group dominate finitely many different homotopy types

Volume 180 / 2003

Danuta Kołodziejczyk Fundamenta Mathematicae 180 (2003), 1-9 MSC: 55P55, 55P15. DOI: 10.4064/fm180-1-1


In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.


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

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