RE: virus: Re: alternative model

Schneider John (
Thu, 12 Dec 1996 02:26:11 -0500

Kenneth Boyd wrote:
> For instance, less than 5 years ago, it was shown that R^4
> [4-D space] has as many distinct "differential structures" as
> the real numbers. In other words, a sufficiently bad choice of
> "differential structure" will make functions you expect to have
> reasonable tangent lines, *fail* to have tangent lines. This is
> unique to 4-D space; for any other [finite-dimensional] space,
> the functions you expect to have tangent lines always do [there
> is effectively only one "differential structure", in terms of
> the functions that have tangent lines.]
> Unfortunately, the proof was nonconstructive: it doesn't tell
> how to construct any of these "weird" spaces.

I assume it's well over my head, but could you give a reference
to the paper which outlined the proof? (I assume that paper will
contain all the other relevant references). I'm interested in
theorems which distinguish between spaces like that. Thanks.

- JPSchneider