论文标题
非压缩4个manifolds的差异组
Diffeotopy groups of non-compact 4-manifolds
论文作者
论文摘要
我们提供有关刺穿4个manifolds的异国平滑平滑差的差异组的信息，从而扩大了异国情调$ \ mathbb {r}^4 $'s的差异组的先前结果。特别是，我们证明，对于可平滑的4个manifold $ m $，对于非空的，离散的点$ s \ subsetneq \ mathring {m} $，$ m \ smalleTsminus s $的差异群是无法算不可计的。 然后，我们证明，对于可平滑的4个manifold $ m $，对于非空的，离散的点$ s \ subsetNeq \ Mathring {m} $，存在$ m \ smalleTseminus s $的平滑性，其差异群具有与$ \ nathcal {r} r} _u $，freed man $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ {r. $ $ $ $ $ $ $ { 此外，我们证明，如果$ m $不太平滑，这两个结果仍然在$ | s |的假设下保持不变。 \ ge 2 $。
We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there are uncountably many distinct smoothings of $M\smallsetminus S$ whose diffeotopy groups are uncountable. We then prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there exists a smoothing of $M\smallsetminus S$ whose diffeotopy groups have similar properties as $\mathcal{R}_U$, Freedman and Taylor's universal $\mathbb{R}^4$. Moreover, we prove that if $M$ is non-smoothable, both results still hold under the assumption that $|S| \ge 2$.
