论文标题
古典和新的水管同源球体边界可缩度的歧管和同源球
Classical and new plumbed homology spheres bounding contractible manifolds and homology balls
论文作者
论文摘要
低维拓扑的一个核心问题询问哪些同源$ 3 $ -SPHERES BOUND-SPHERIBLIBLE $ 4 $ -MANIFOLDS或同源性$ 4 $ -BALLS。在本文中，我们将这个问题用于$ 3 $ - manifolds，并提出了两个新的无限家庭。我们考虑了大约十九八十年代的大多数古典示例，通过谴责它们都绑定了Mazur歧管。我们还表明，几个著名的家庭可能会有不同类型的$ 4 $ manifolds，称为Poénaru同源性$ 4 $ - ball。为了以相当简单的方式统一古典和新结果，我们修改了Mazur的论点，并与Poénaru歧管一起工作。
A central problem in low-dimensional topology asks which homology $3$-spheres bound contractible $4$-manifolds or homology $4$-balls. In this paper, we address this question for plumbed $3$-manifolds and we present two new infinite families. We consider most of the classical examples from around the nineteen eighties by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of $4$-manifolds, called Poénaru homology $4$-balls. To unify classical and new results in a fairly simple way, we modify Mazur's argument and work with Poénaru manifolds.
