Alexandre Gabard
Published 2006-09-23Version 1
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.
Comments: 5 pages, 3 figures
Homotopy types of homeomorphism groups of noncompact 2-manifolds
Homotopy types of the components of spaces of embeddings of compact polyhedra into 2-manifolds
Homotopy type of stabilizers of circle-valued functions with non-isolated singularities on surfaces
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