Sure, let's hear it. On Fri, Apr 24, 2015 at 9:51 AM, Dan Asimov <asimov@msri.org> wrote:
It's been known since 1962 that all Euclidean spaces R^n for n <> 4 have only one smooth structure (up to equivalence). In 1982 it was discovered that R^4 has a nonstandard smooth structure.
I've long wanted to understand why there can be nonstandard smooth structures on R^4, though no other R^n has anything but the usual one (up to diffeomorphism).
The book "The Wild World of 4-Manifolds" by Alexandru Scorpan has explained it so clearly that I almost feel I get at least a sketch of the main argument, modulo some major results.
If anyone is interested, I'll post a sketch of the proof. (And the statement of major results which it is modulo.)
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