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].
Keywords:
proper homotopy type properly c connected locally finite n dimensional cw complex represented closed polyhedron mathbb n c theorem n c geq special general proper homotopy embedding theorem theorem n c leq basic properties proper algebraic topology which summarized appendices results paper proper analogues classical results stallings wall finite cw complexes see drani nikov repov
Affiliations des auteurs :
M. Cárdenas
1
;
T. Fernández
1
;
F. F. Lasheras
1
;
A. Quintero
1
1
Departamento de Geometría y Topología Facultad de Matemáticas Universidad de Sevilla Apartado 1160 41080 Sevilla, Spain
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title = {Embedding proper homotopy types},
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M. Cárdenas; T. Fernández; F. F. Lasheras; A. Quintero. Embedding proper homotopy types. Colloquium Mathematicum, Tome 95 (2003) no. 1, pp. 1-20. doi: 10.4064/cm95-1-1
