论文标题
关于同源飞机和可签定的$ 4 $ - manifolds
On homology planes and contractible $4$-manifolds
论文作者
论文摘要
如果它既界限同源平面，又是mazur或poénaru歧管，我们将其称为非平凡的同源性领域。在1980年，柯比（Kirby）通过证明了拉马努杰（Ramanujam）表面的边界界定了一个mazur歧管，从而找到了第一个例子，从那以后，它一直是一个例子。通过追踪他们的初始步骤，我们提供了第一个其他示例，并提出了三个无限的Kirby-Ramanujam球体。另外，我们表明，我们的柯比·拉马努贾姆（Kirby-Ramanujam）领域中的一个家庭对布里斯科恩（Brieskorn Spheres）的两个家族的拼接是不同的。由于这个Kirby-Ramanujam家族的范围为$ 4 $ -Manifolds，因此它们位于同源性共同体小组中的琐碎元素的类别中；但是，两个剪接组件在该组中分别是线性独立的。
We call a non-trivial homology sphere a Kirby-Ramanujam sphere if it bounds both a homology plane and a Mazur or Poénaru manifold. In 1980, Kirby found the first example by proving that the boundary of the Ramanujam surface bounds a Mazur manifold and it has remained a single example since then. By tracing their initial step, we provide the first additional examples and we present three infinite families of Kirby-Ramanujam spheres. Also, we show that one of our families of Kirby-Ramanujam spheres is diffeomorphic to the splice of two certain families of Brieskorn spheres. Since this family of Kirby-Ramanujam spheres bound contractible $4$-manifolds, they lie in the class of the trivial element in the homology cobordism group; however, both splice components are separately linearly independent in that group.
