We call an integral homology sphere $\textit{non-trivially}$ bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example $\Sigma(2,3,7)$, Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: $\Sigma(2,4n+1,12n+5)$ and $\Sigma(3,3n+1,12n+5)$ for odd $n$. Using their technique, we present new such families: $\Sigma(2,4n+3,12n+7)$ and $\Sigma(3,3n+2,12n+7)$ for even $n$. Also manipulating their main argument, we simply recover some classical results of Akbulut and Kirby, Fickle, Casson and Harer, and Stern about Brieskorn spheres bounding integral homology balls.

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更多 Brieskorn 球体包围有理球

我们称一个积分同调球 $\textit{non-trivially}$ 限制了一个有理同调球，如果它被阻止限制一个积分同调球。在 Fintushel 和 Stern 的著名例子 $\Sigma(2,3,7)$ 之后，Akbulut 和 Larson 最近提供了 Brieskorn 球体的第一个无限族非平凡有理有理同源球：$\Sigma(2,4n+1, 12n+5)$ 和 $\Sigma(3,3n+1,12n+5)$ 为奇数 $n$。使用他们的技术，我们提出了新的此类系列：$\Sigma(2,4n+3,12n+7)$ 和 $\Sigma(3,3n+2,12n+7)$ 甚至 $n$。同样操纵他们的主要论点，我们简单地恢复了 Akbulut 和 Kirby、Fickle、Casson 和 Harer 以及 Stern 关于 Brieskorn 球体包围积分同源球的一些经典结果。