论文标题
$ \＃^n \ mathbb {c} p^2 $中的球形配置
Configurations of spheres in $\#^n \mathbb{C} P^2$
论文作者
论文摘要
通过在连接的$ \ mathbb {c} p^2 $的连接总和中获取球形管道的嵌入补充，我们构建了简单地连接了具有镜头空间边界和$ b_2 = 1 $的四个manifolds的示例。最终的边界包括许多镜头空间，这些镜头空间不能来自$ s^3 $的任何结上的整数手术，因此不能通过将单个双手柄连接到$ b^4 $来构建相应的四个manifolds。使用类似的构造，我们给出了一个以$ \＃^4 \ mathbb {c} p^2 $为$ 20 $的嵌入式球体的示例，并猜想这是最大值。
By taking the complements of embeddings of sphere plumbings in connected sums of $\mathbb{C} P^2$, we construct examples of simply connected four-manifolds with lens space boundary and $b_2 = 1$. The resulting boundaries include many lens spaces that cannot come from integer surgery on any knot in $S^3$, so the corresponding four-manifolds cannot be built by attaching a single two-handle to $B^4$. Using similar constructions, we give an example of an embedded sphere in $\#^4 \mathbb{C} P^2$ with self-intersection number $20$, and conjecture that this is the maximum possible.
