Smoothing theory revisited
Algebraic Topology
2010-07-09 v2 Geometric Topology
Abstract
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
Cite
@article{arxiv.1006.2189,
title = {Smoothing theory revisited},
author = {John R. Klein and Bruce Williams},
journal= {arXiv preprint arXiv:1006.2189},
year = {2010}
}
Comments
This paper has been withdrawn by the authors. The proof of the verification of axiom 1 for the smoothing functor that is given in the paper is false, since it would violate what is known in dimension 4. If U is a subset of V and both are diffeomorphic to R^4, then the restriction map of smoothing spaces sm(V) -> sm(U) need not be one-to-one on path components. Thus axiom 1 is violated in dimension 4. The verification of axiom 1 in higher dimensions is probably a consequence of the product structure theorem