论文标题
关于符号4个manifolds中3个manifolds的嵌入的注释
A note on embeddings of 3-manifolds in symplectic 4-manifolds
论文作者
论文摘要
我们表明，任何封闭的3个manifold都可以在某些简单连接的封闭符号4个manifold中拓扑嵌入，并且在一次稳定后可以使其成为平滑的嵌入。作为证据的推论，我们表明同源性共同体小组是由Stein folable 3-manifolds产生的。我们还发现了平滑嵌入的障碍物：存在3个manifolds，无法以适当尊重弱凸边界的任何合成歧管中适当尊重取向的方式平滑嵌入。这种嵌入障碍物也可用于检测4个manifolds上的外来平滑结构。
We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that the homology cobordism group is generated by Stein fillable 3-manifolds. We also find obstructions on smooth embeddings: there exists 3-manifolds which cannot smoothly embed in a way that appropriately respect orientations in any symplectic manifold with weakly convex boundary. This embedding obstruction can also be used to detect exotic smooth structures on 4-manifolds.
