Polyhedra with finite fundamental group dominate finitely many different homotopy types

Danuta Kołodziejczyk. "Polyhedra with finite fundamental group dominate finitely many different homotopy types." Fundamenta Mathematicae 180.1 (2003): 1-9. <http://eudml.org/doc/283080>.

@article{DanutaKołodziejczyk2003,
abstract = {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.},
author = {Danuta Kołodziejczyk},
journal = {Fundamenta Mathematicae},
keywords = {shape type; homotopy type; polyhedron; shape or homotopy domination},
language = {eng},
number = {1},
pages = {1-9},
title = {Polyhedra with finite fundamental group dominate finitely many different homotopy types},
url = {http://eudml.org/doc/283080},
volume = {180},
year = {2003},
}

TY - JOUR
AU - Danuta Kołodziejczyk
TI - Polyhedra with finite fundamental group dominate finitely many different homotopy types
JO - Fundamenta Mathematicae
PY - 2003
VL - 180
IS - 1
SP - 1
EP - 9
AB - 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.
LA - eng
KW - shape type; homotopy type; polyhedron; shape or homotopy domination
UR - http://eudml.org/doc/283080
ER -