Heegaaed分解有不交曲线性质的一个充分条件

Sufficient Conditions for Heegaard Splittings with Disjoint Curve Property

中文关键词:  Heegaard分解  不交曲线性质.

英文关键词:Heegaard splitting  disjoint curve property.

中文摘要:

      本文给出Heegaard分解有不交曲线性质的两个充分条件, 具体如下:设$(C_1,C_2;F)$为亏格$\geq 2$的强不可约的Heegaard分解, $D_i$ 为$C_i$ 中的本质圆片, $i=1,2$, 若下列条件之一成立: (1) $\partial D_1$和$\partial D_2$之一在$F$上分离,且$|\partial D_1 \cap\partial D_2 |\leq 2g-1$；（2） $\partial D_1$ 和$\partial D_2 $ 在$F$上均不分离,且$

英文摘要:

      In the paper, we give two conditions that the Heegaard splitting admits the disjoint curve property. The main result is that for a genus $g~(g\geq 2)$ strongly irreducible Heegaard splitting $(C_1,C_2;F)$, let $D_i$ be an essential disk in $C_i$, $i=1,2$, satisfying (1) at least one of $\partial D_1$ and $\partial D_2$ is separating in $F$ and $|\partial D_1 \cap \partial D_2 |\leq 2g-1$; or (2) both $\partial D_1$ and $\partial D_2 $ are non-separating in $F$ and $|\partial D_1 \cap \partial D_2 |\leq 2g-2 $, then $(C_1,C_2;F)$ has the disjoint curve property.