Building off of the work of Kervaire–Milnor and Hill–Hopkins–Ravenel, Wang and Xu showed that the only odd dimensions $n$ for which $S^n$ has a unique differentiable structure are 1, 3, 5, and 61. We show that the only even dimensions below 140 for which $S^n$ has a unique differentiable structure are 2, 6, 12, 56, and perhaps 4.

中文翻译：

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使用焦化器J检测低尺寸的奇异球体

Wang和Xu在Kervaire-Milnor和Hill-Hopkins-Ravenel的工作基础上，发现唯一的奇数维 $ñ$ 为此 ${\mathrm{小号}}^{ñ}$ 具有独特的可微结构，分别是1、3、5和61。我们证明，对于 ${\mathrm{小号}}^{ñ}$ 具有独特的可微结构的是2、6、12、56，也许是4。