A separable manifold failing to have the homotopy type of a CW-complex
Geometric Topology
2007-05-23 v1
Abstract
We show that the Pr\"ufer surface, which is a separable non-metrizable 2-manifold, has not the homotopy type of a CW-complex. This will follow easily from J. H. C. Whitehead's result: if one has a good approximation of an arbitrary space by a CW-complex, which fails to be a homotopy equivalence, then the given space is not homotopy equivalent to a CW-complex.
Cite
@article{arxiv.math/0609665,
title = {A separable manifold failing to have the homotopy type of a CW-complex},
author = {Alexandre Gabard},
journal= {arXiv preprint arXiv:math/0609665},
year = {2007}
}
Comments
5 pages, 3 figures