边界稳定化Heegaard曲面具有临界性的一个必要条件  

A Necessary Condition for the Boundary Stabilized Heegaard Surfaces to be Critical

作　　者：孙艳红[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028000

出　　处：《湖北民族学院学报（自然科学版）》2013年第3期282-284,288,共4页Journal of Hubei Minzu University(Natural Science Edition)

摘　　要：拓扑极小曲面是三维流形中一类重要的曲面,由David Bachman首次提出,其中,指数为2的拓扑极小曲面称为临界曲面,它是一类弱可约曲面,但具有类似不可压缩曲面和强不可约曲面的性质,在Lee Jung Honn工作的基础上,证明了边界稳定化后的Heegaard曲面是临界曲面时,原来的Heegaard曲面具有不交线性质.Topologically minimal surfaces, which were introduced by David Bachman, are important sur- faces embeded in 3-manifolds. Moreover, topologically minimal surfaces with index 2 are called critical surfaces. Critical surfaces are weakly reducible surfaces, but with the similar properties as incompressible surfaces and strongly irreducible surfaces. In this paper, we show if a boundary stabilized Heegaard sur- face is critical, then the original Heegaard splitting has the disjoint curves property.

关 键 词：拓扑极小曲面 临界区面 边界稳定化 HEEGAARD分解 

分 类 号：O189[理学—数学]