Embedding proper homotopy types

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

Colloquium Mathematicum, Tome 95 (2003) no. 1, pp. 1-20

Résumé

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].

Détail

DOI : 10.4064/cm95-1-1

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