3维流形中的双侧可压缩曲面与薄形分解  

Bicompressible Surfaces in 3-Manifolds and Thin Position

作　　者：张明星[1] 邱瑞锋[1] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024

出　　处：《数学年刊（A辑）》2008年第3期307-314,共8页Chinese Annals of Mathematics

基　　金：高等学校博士学科点专项科研基金(No.20050141011)资助的项目

摘　　要：对一个3维流形的任何一组彼此不相交的非过剩的双侧可压缩曲面集所含有的元素个数证明了是有上界的,记为N_0(M),记L_0(M)为M的薄形分解的长度,则有L_0(M)≤N_0(M)+|(■)M|,记L_0(V∪W)为M的Heegaard分解M=V∪W的薄形分解的长度,则对M的任意不可稳定化的Heegaard分解都有L_0(V∪W)≤N_0(W)+|(■)M|.This paper first proves that any non-excessive set of completely disjoint essential bicompressible surfaces in a 3-manifold M contains finitely many elements,furthermore it has an upper bound N0（M）.Denoted by L0（M）of length of thin position of M,the authors prove that L0（M）≤N0（M）＋｜（δ）M｜.Denoted by L0（V∪W）the length of thin position of the Heegaard splitting M=V∪W,L0（V∪W）≤N0（M）＋｜（δ）M｜for any unstabilized Heegaard splittings of M is proved.

关 键 词：双侧可压缩曲面 HEEGAARD分解 薄形分解 

分 类 号：O189.31[理学—数学]