Embedding proper homotopy types
Volume 95 / 2003
Colloquium Mathematicum 95 (2003), 1-20
MSC: Primary 55P57, 57Q35; Secondary 57Q91.
DOI: 10.4064/cm95-1-1
Abstract
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].
