论文标题
整体klein瓶手术和Heegaard浮子同源
Integral Klein bottle surgeries and Heegaard Floer homology
论文作者
论文摘要
我们研究的是，其中包含一个klein瓶的$ x $封闭，连接，定向的三个manifolds $ x $，作为$ s^3 $的结的整体手术。这样的$ x $可以作为扭曲的$ i $块粘合在klein瓶上的粘合，并使用各种Heegaard Floer型不变性来产生手术障碍物。假设$ x $是沿两个结属的$ 8 $ surgery，并且是通过将扭曲的$ i $ undle粘在克莱因瓶上的$ s^3 $结的补充而产生的。我们表明$ x $是L型，它一定是二歧管$ \ left（-1; \ tfrac {1} {2} {2}，\ tfrac {1} {2} {2}，\ tfrac {2} {2} {5} {5} {5} {5} \ right）$，并且必须为$ k = t（2,5）。
We study which closed, connected, orientable three-manifolds $X$ containing a Klein bottle arise as integral Dehn surgery along a knot in $S^3$. Such $X$ are presentable as a gluing of the twisted $I$-bundle over the Klein bottle to a knot manifold, and we use a variety of Heegaard Floer type invariants to generate surgery obstructions. Suppose that $X$ is $8$-surgery along a genus two knot, and arises by gluing the twisted $I$-bundle over the Klein bottle to an $S^3$ knot complement. We show that $X$ is an L-space, it must be the dihedral manifold $\left(-1; \tfrac{1}{2}, \tfrac{1}{2}, \tfrac{2}{5}\right)$, and the surgery knot must be $K=T(2,5)$.
