Motivated by Akbulut-Larson's construction of Brieskorn spheres bounding rational homology 4-balls, we explore plumbed 3-manifolds that bound rational homology circles and use them to construct infinite families of rational homology 3-spheres that bound rational homology 4-balls. Some of these rational homology 3-spheres are new examples of integer homology 3-spheres that bound rational homology 4-balls, but do not bound integer homology 4-balls (i.e. nontrivial elements of $\text{ker}({\mathrm{\Theta }}_{\mathbb{Z}}^3\to {\mathrm{\Theta }}_{\mathbb{Q}}^3)$). In particular, we find infinite families of torus bundles over the circle that bound rational homology circles, provide a simple method for constructing more general plumbed 3-manifolds that bound rational homology circles, and show that, for example, −1-surgery along any unknotting number one knot K with a positive crossing that can be switched to unknot K bounds a rational homology 4-ball.

受Akbulut-Larson构造包围理性同构4球的Brieskorn球体的启发，我们探索了约束理性同构圆的垂直3流形，并使用它们构造了约束理性同构4球的无限族理性同构3球。其中一些有理同构3球是整数同构3球的新示例，它们绑定有理同构4球，但不绑定整数同构4球（即$\text{克尔}（{\mathrm{\Theta }}_{\mathbb{ž}}^3\to {\mathrm{\Theta }}_{\mathbb{问}}^3）$）。特别是，我们在绑定有理同源性圆的圆上找到了无限的圆环束族，提供了一种简单的方法来构造约束有理同源性圆的更一般的铅垂3型流形，并显示，例如，沿着任何方向的-1手术unknotting头号结ķ具有正交叉，可以被切换到unknot ķ界定一个合理的同源四球。