论文标题
将球体嵌入结迹
Embedding spheres in knot traces
论文作者
论文摘要
$ s^3 $打结的$ n $ - 框架手术的痕迹是4个Manifold同型，相当于2-Sphere。我们表征了当局部嵌入的2速段的第二个同型组的发电机可以实现其补充具有Abelian基本组的局部嵌入式2杆时。我们的表征是在经典和可计算的三维结中。对于每个$ n $，这提供了暗示结上是拓扑上的$ n $ shake片的条件，这与弗里德曼和奎因的结果直接相似，即用琐碎的亚历山大多项式的结节在拓扑上是切成薄片。
The trace of $n$-framed surgery on a knot in $S^3$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable 3-dimensional knot invariants. For each $n$, this provides conditions that imply a knot is topologically $n$-shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice.
