中文摘要：

主要研究压缩体上的完全圆片系统和带边可定向的三维流形的强不可约的Heegaard分解。偏倒d＋W表示压缩体形的正边界。找到了压缩体形的完全圆片系统，并且证明了真嵌入到W中且边界在偏倒d＋W上的任何本质圆片都可以由压缩体的这个圆片系统中的圆片的连通和表示出来。进一步研究了曲面偏倒d＋W上与柄体的每一个圆片至少交n次的简单闭曲线，给出了一个判定简单闭曲线是n闭的一个有限的组合条件，并且给出一个带边的可定向的三维流形的Heegaard分解是强不可约的判定条件。

英文摘要：

The authors investigate a complete disk systems of a compression body and the strongly irreducible Heegaard splitting of a boundary orientable 3-manifold. A surface 偏倒d W is a positive boundary of a compression body W. They find a complete disk system of a compression body W, and prove any embedded essential disk in W whose boundary lies in 偏倒d ＋ W can be built as iterated connected sum of the disks in the complete disk system of a compression body. Furthermore, they look at simple closed curves on 偏倒d ＋ W which intersect every disk in the compression body at least n times. They give a finite criterion for a curve to be n-closed and derive a sufficiency condition for a Heegaard splitting of a boundary orientable 3-manifold to be strongly irreducible.