论文标题
亚稳态范围内的惯性组
Inertia groups in the metastable range
论文作者
论文摘要
我们证明，所有足够连接的高维$（2N）$ - 歧管的惯性组都是微不足道的。这是在亚稳态范围内的一般歧管迈出的关键步骤。具体来说，对于$ m \ gg 0 $和$ k> 5/12 $，假设$ m $是$ \ lfloor km \ rfloor $ - 连接，平滑，封闭，定向，定向$ m $ - manifold，$σ$是一个异国情调的$ m $ - $ m $ -sphere。我们证明，如果$ m \sharpσ$不合格至$ m $，则$σ$限制了可行的可行流形。我们的证明是基于对PstrąGowski的合成光谱类别中第二次扩展功率函数的理解。
We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2n)$-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for $m \gg 0$ and $k>5/12$, suppose $M$ is a $\lfloor km \rfloor$-connected, smooth, closed, oriented $m$-manifold and $Σ$ is an exotic $m$-sphere. We prove that, if $M \sharp Σ$ is diffeomorphic to $M$, then $Σ$ bounds a parallelizable manifold. Our proof is built on an understanding of the second extended power functor in Pstrągowski's category of synthetic spectra.
