Sufficient Conditions for Heegaard Splittings with Disjoint Curve Property

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■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 ■D_1 and ■D_2 is separating in F and|■D_1∩■D_2|■2g-1;or(2)both ■D_1 and ■D_2 are non-separating in F and|■D_1∩■D_2|■2g-2,then(C_1,C_2;F)has the disjoint curve property.