论文标题
透镜空间的确定填充物
Definite fillings of lens spaces
论文作者
论文摘要
本文考虑了确定透镜空间的最小（通过第二个贝蒂数量测量）的最小（按第二贝蒂数量测量）的问题。主要的结果是对相关的负定规范管道的那些晶状体空间进行分类。如果相应的4个manifold最少，则分类以10个“禁止”子图的列表的形式无法显示在管道图中。我们还表明，每当管道最小化时，给定镜头空间的任何其他负定填充物都具有相同的交叉点形式，直到添加对角线汇总。还讨论了4个manifolds中透镜空间平滑嵌入的后果。
This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classify those lens spaces for which the associated negative-definite canonical plumbing is minimal. The classification takes the form of a list of 10 "forbidden" subgraphs that cannot appear in the plumbing graph if the corresponding plumbed 4-manifold is minimal. We also show that whenever the plumbing is minimal any other negative-definite filling for the given lens space has the same intersection form up to addition of diagonal summands. Consequences regarding smooth embeddings of lens spaces in 4-manifolds are also discussed.
