复杂三维流形的两类四穿孔球面和  

Two classes of four-punctured sphere sum of complicated three manifolds

作　　者：王树新[1] 冷健[1] 魏义婷 王霄[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2016年第4期458-461,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金面上资助项目(11471151);辽宁省博士科研启动基金资助项目(20141101)

摘　　要：在邱瑞锋、王诗宬和张明星证明了可定向闭曲面加厚及某些复杂三维流形的平环和具有亏格可加性的基础之上,从2个可定向闭曲面加厚沿着不可压缩四穿孔球面进行黏合出发,利用三维流形组合拓扑的讨论技巧和方法,通过分析四穿孔球面在相黏可定向闭曲面加厚上的2种不同分离形式,证明了可定向闭曲面加厚及某些复杂三维流形的两类四穿孔球面和具有亏格可加性,将复杂三维流形某些带边曲面和具有亏格可加性推广到更加一般的情形.Ruifeng Qiu,Shicheng Wang and Mingxing Zhang proved that the genera of thickened orientable closed surfaces and some complicated three manifolds are additive under annular sum.Based on their results,we mainly use the combinatorial techniques and methods of 3-manifolds to analyze and discuss the four punctured sphere sum of thickened orientable closed surfaces.We prove that the genera of thickened orientable closed surfaces and some complicated three manifolds are additive under two classes of four-punctured sphere sum,and we generalize the additivity of genus of some punctured sphere sum of complicated three manifolds.

关 键 词：压缩体 HEEGAARD分解 亏格 

分 类 号：O189.3[理学—数学]