I was doing more reading in John Lee's "Introduction to smooth manifolds" and he mentioned that for every [itex] n \in \mathbb{N} [/itex] such that [itex] n \neq 4 [/itex], the smooth structure that can be imposed on [itex] \mathbb{R}^n [/itex] is unique up to diffeomorphism, but for [itex] \mathbb{R}^4 [/itex], there are uncountably many smooth structures, none of which are diffeomorphic to another. Why is this so? What makes 4-space so special? I know that the full answer to this question is beyond my scope (for now), but I was hoping for a laymens answer.(adsbygoogle = window.adsbygoogle || []).push({});

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# Unique smooth structure on Euclidean space

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