压缩体上圆片系统和曲面上的曲线的交

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(δ) W表示压缩体W的正边界.找到了压缩体W的完全圆片系统,并且证明了真嵌入到W中且边界在(δ) 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(δ) 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.

Intersections of curves on surfaces with disk systems in compression bodies

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 (δ)+ 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 (δ)+ 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 (δ)+ 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.