24 Apr
2015
24 Apr
'15
10:52 a.m.
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.) --Dan