论文标题
$（n-1）$ - 连接$ 2N $ - manifolds的惯性组
Inertia groups of $(n-1)$-connected $2n$-manifolds
论文作者
论文摘要
在本文中，我们计算了$（N-1）$连接的惯性组，平稳，封闭，定向$ 2N $ -Manifolds，其中$ n \ geq 3 $。结果，我们完成了这种流形的差异分类，完成了六十年前沃尔发起的计划，除了克尔瓦尔不变的一个问题的$ 126 $维度案例外。 特别是，我们发现惯性集团总是以$ n \ neq 4,8,9 $的质量消失 - $ n \ gg 0 $，这是由以前的几位作者（包括Wall，Stolz和Burklund and Burklund and Hahn）和第一位命名作者所知道的。当$ n = 4,8,9 $时，我们应用了克雷克（Kreck）的改良手术和纳吉（Nagy）证明的克劳利（Crowley）的$ q $ form猜想的特殊情况，以计算这些歧管的惯性组。在$ n = 4,8 $的情况下，我们的结果收回了克劳利（Nagy）和克劳利（Crowley）的未发表的作品 - olbermann。 相比之下，我们表明，$（n-1）$的同质和一致性惯性组，连接，平滑，封闭，定向$ 2N $ -Manifolds，$ n \ geq 3 $总是消失。
In this paper, we compute the inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds where $n \geq 3$. As a consequence, we complete the diffeomorphism classification of such manifolds, finishing a program initiated by Wall sixty years ago, with the exception of the $126$-dimensional case of the Kervaire invariant one problem. In particular, we find that the inertia group always vanishes for $n \neq 4,8,9$ -- for $n \gg 0$, this was known by the work of several previous authors, including Wall, Stolz, and Burklund and Hahn with the first named author. When $n = 4,8,9$, we apply Kreck's modified surgery and a special case of Crowley's $Q$-form conjecture, proven by Nagy, to compute the inertia groups of these manifolds. In the cases $n=4,8$, our results recover unpublished work of Crowley--Nagy and Crowley--Olbermann. In contrast, we show that the homotopy and concordance inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds with $n \geq 3$ always vanish.
