Sufficient Conditions for Heegaard Splittings with Disjoint Curve Property  

作　　者：尹逊波 雷逢春 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology,Heilongjiang 150001,China [2]Depatment of Applied Mathematics,Dalian University of Technology,Liaoning 116024,China

出　　处：《Journal of Mathematical Research and Exposition》2008年第2期435-438,共4页数学研究与评论（英文版）

基　　金：Foundation item： the National Natural Science Foundation of China （No. 10571034）

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.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（C1,C2;F）,let Di be an essential disk in Ci,i=1,2,satisfying（1）at least one of δD1 and δD2 is separating in F and｜δD1∩δD2｜≤2g-1;or（2）both δD1 and δD2 are non-separating in F and｜δD1∩δD2｜≤2g-2,then（C1,C2;F）has the disjoint curve property.

关 键 词：Heegaard splitting disjoint curve property 

分 类 号：O189.21[理学—数学]