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 ...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.展开更多
基金Foundation item： the National Natural Science Foundation of China （No. 10571034）
文摘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.
