一类θ-曲线补空间中IPI曲面性质研究  

Research on the properties of IPI surfaces in a class ofθ-curve complements

作　　者：王树新[1] 王佳琦 姜蕾 WANG Shuxin;WANG Jiaqi;JIANG Lei(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学,数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报(自然科学版)》2025年第1期74-79,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省属本科高校基本科研业务费专项资金资助项目(LJ212410165006)。

摘　　要：三维流形中不同类型曲面的性质及其分类历来都是三维流形理论研究的核心和热点问题.纽结、链环和空间图理论在三维流形理论中占据不可或缺的地位.20世纪80年代以来,纽结、链环和空间图补空间中不可压缩配对不可压缩(IPI)曲面的性质及其对应约化拓扑图的具体构成形式是纽结、链环和空间图研究的一个重要课题.将W.Me-nasco和C.Adams给出的研究纽结、链环和空间图补空间中IPI曲面性质的方法与空间中一类θ-曲线相结合,在不限定这类θ-曲线补空间中连通IPI曲面子午线边界分支数的条件下,通过三维流形组合拓扑的方法分析该曲面处于标准位置时其对应约化拓扑图中曲线分支的走势,证明相应曲面均为穿孔球面且F∩S_(2)^(+)仅有一个分支,其字表示为p^(i)(i≥2,i∈ℕ_(+)).The properties and classifications of different types of surfaces in three-dimensional manifold have always been the core and hot issues in three-dimensional manifold theory.Knot,link and spatial graph theory play an indispensable role in the theory of three-dimensional manifold.Since the 1980s,the properties of incompressible and pairwise incompressible(IPI)surfaces in knot,link and spatial graph complement,and the constitution form of the corresponding reducible topological graphs have been important topics in the study of knot,link and spatial graph theory.In this paper,the method given by W.Menasco and C.Adams to study the properties of IPI surfaces in the complements of knot,link and spatial graph is combined with a class ofθ-curves in space.Under the condition of not limiting the meridian boundary component number of the connected IPI surfaces in this class ofθ-curve complements,by the method of three-dimensional manifold combination topology,the trend of the curves in the reducible standard topological graph of connected IPI surfaces in the correspondingθ-curve complements is analyzed is proren that the corresponding surfaces are punctured spheres,F∩S^(2)_(+)has only one component and its word representation is p^(i)(i≥2,i∈ℕ_(+)).

关 键 词：θ-曲线 约化拓扑图 穿孔球面 字表示 

分 类 号：O189.24[理学—数学]