论文标题
$ 4 $ - 具有边界和基本组$ \ mathbb {z} $的manifolds
$4$-manifolds with boundary and fundamental group $\mathbb{Z}$
论文作者
论文摘要
在边界上的某些假设下，我们将拓扑$ 4 $ manifolds与边界和基本组$ \ Mathbb {z} $分类。我们将其应用于简单连接的$ 4 $ - manifolds，其中$ s^3 $边界，其中表面补充的基本组为$ \ mathbb {z} $。然后，我们将这些同态分类与平滑设置进行比较。对于歧管，我们表明，每种冬季式形式都以$ \ mathbb {z} [t^{\ pm 1}] $作为一对具有边界和基本组$ \ mathbb {z z} $的奇异平滑的4个manifolds的Equivariant相交形式出现。对于表面，我们也有类似的结果，特别是我们表明，每$ 2 $ handleboby带有$ s^3 $边界都包含一对外来盘。
We classify topological $4$-manifolds with boundary and fundamental group $\mathbb{Z}$, under some assumptions on the boundary. We apply this to classify surfaces in simply-connected $4$-manifolds with $S^3$ boundary, where the fundamental group of the surface complement is $\mathbb{Z}$. We then compare these homeomorphism classifications with the smooth setting. For manifolds, we show that every Hermitian form over $\mathbb{Z}[t^{\pm 1}]$ arises as the equivariant intersection form of a pair of exotic smooth 4-manifolds with boundary and fundamental group $\mathbb{Z}$. For surfaces we have a similar result, and in particular we show that every $2$-handlebody with $S^3$ boundary contains a pair of exotic discs.
