Heegaaed分解有不交曲线性质的一个充分条件

In the paper,we give two conditions that the Heegaard splitting admits the disjoint cnrve property.The main result is that for a genus g(g≥2)strongly irreducible Heegaard splitting(C1,C2;F),let Di be an essential disk in Ci,i=1,2,satisfying(1)at least one of (の)D4 and (の)D2 is separating in F and |(の)D1 (∩)(の)D2|≤ 2g-1;or(2)both (の)D1 and (の)D2 are non-separating in F and |(の)D1 (∩)(の)D2|≤ 2g-2,then(C1,C2;F)has the disjoint curve property.

Sufficient Conditions for Heegaard Splittings with Disjoint Curve Property

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.