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 (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 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].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-1,
author = {M. C\'ardenas and T. Fern\'andez and F. F. Lasheras and A. Quintero},
title = {Embedding proper homotopy types},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {1-20},
zbl = {1038.55008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-1}
}
M. Cárdenas; T. Fernández; F. F. Lasheras; A. Quintero. Embedding proper homotopy types. Colloquium Mathematicae, Tome 96 (2003) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-1/