# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Embedding proper homotopy types

### Tom 95 / 2003

Colloquium Mathematicum 95 (2003), 1-20 MSC: Primary 55P57, 57Q35; Secondary 57Q91. DOI: 10.4064/cm95-1-1

#### Streszczenie

We show that the proper homotopy type of any properly $c$-connected locally finite $n$-dimensional CW-complex is represented by a closed polyhedron in ${\mathbb R}^{2n-c}$ (Theorem I). The case $n-c\geq 3$ is a special case of a general proper homotopy embedding theorem (Theorem II). For $n-c\leq 2$ we need some basic properties of “proper" algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite CW-complexes; see also Dranišnikov and Repovš [7].

#### Autorzy

• M. CárdenasDepartamento de Geometría y Topología
41080 Sevilla, Spain
• T. FernándezDepartamento de Geometría y Topología
41080 Sevilla, Spain
• F. F. LasherasDepartamento de Geometría y Topología
41080 Sevilla, Spain
• A. QuinteroDepartamento de Geometría y Topología