论文标题
在有限的Heegaard分裂上，许多不相交的压缩磁盘
On Heegaard splittings with finite many pairs of disjoint compression disks
论文作者
论文摘要
假设$ v \ cup_s w $是封闭的3个manifold的弱还原的Heegaard拆分，该分裂仅承认$ n $ n $对在不同侧面的分离压缩磁盘，$ g> 2 $。我们显示$ v \ cup_s w $承认一个未取消的操作：$（v_1 \ cup_ {s_1} w_1）\ cup_f（w_2 \ cup_ {s_2} v_2）$，这样$ w_i $只有一个分开的压缩disk和$ d（s_i）\ geq 2 $，如果$ n> 1 $，则至少有$ d（s_i）$中的一个为2，而$ s $是关键的Heegaard表面。
Suppose $V\cup_S W$ is a weakly reducible Heegaard splitting of a closed 3-manifold which admits only $n$ pairs of disjoint compression disks on distinct sides and $g>2$. We show $V\cup_S W$ admits an untelescoping: $(V_1\cup_{S_1}W_1)\cup_F(W_2\cup_{S_2}V_2)$ such that $W_i$ has only one separating compressing disk and $d(S_i)\geq 2$, for $i=1,~2$. If $n>1$, at least one of $d(S_i)$ is 2 and $S$ is a critical Heegaard surface.
