Homotopy dominations within polyhedra

Danuta Kołodziejczyk. "Homotopy dominations within polyhedra." Fundamenta Mathematicae 178.3 (2003): 189-202. <http://eudml.org/doc/283186>.

@article{DanutaKołodziejczyk2003,
abstract = {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.},
author = {Danuta Kołodziejczyk},
journal = {Fundamenta Mathematicae},
keywords = {shape or homotopy domination; compactum; polyhedron; capacity; depth},
language = {eng},
number = {3},
pages = {189-202},
title = {Homotopy dominations within polyhedra},
url = {http://eudml.org/doc/283186},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Danuta Kołodziejczyk
TI - Homotopy dominations within polyhedra
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 3
SP - 189
EP - 202
AB - 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.
LA - eng
KW - shape or homotopy domination; compactum; polyhedron; capacity; depth
UR - http://eudml.org/doc/283186
ER -