复杂三维流形简单穿孔球面和的亏格可加性

发布时间：2018-04-02 23:18

本文选题：不可压缩曲面　切入点：三穿孔球面和　出处：《辽宁师范大学》2015年硕士论文

【摘要】：众所周知,三维流形沿曲面相粘亏格的可加性、三维流形中不可压缩曲面的分类、纽结的分类是三维流形理论的三个核心问题.特别地,给出三维流形中不可压缩曲面的分类对于研究三维流形的亏格可加性和纽结的分类具有极其重要的作用.本论文从研究闭曲面I-丛三穿孔球面和及闭曲面I-丛特定类型穿孔球面和出发,给出了闭曲面I-丛某些简单穿孔球面和具有亏格可加性的一系列充分性条件;利用闭曲面I-丛简单穿孔球面和具有亏格可加性的结果,本论文深入分析和讨论了复杂三维流形穿孔球面和是否具有亏格可加性,给出了某些复杂三维流形特定简单带边曲面和具有亏格可加性的充分性条件.即如果Mi是一个紧致的可定向三维流形,Fi是Mi(i=1,2)边界上的一个不可压缩带边曲面,f是F1到F2一个同胚.对于具有特定条件的相粘曲面Fi,如果Mi具有一个Heegaard距离至少是2(g(M1)+g(M2))+1的Heegaard分解,则g(M)=g(M1)+g(M2).
[Abstract]:It is well known that the additivity of three dimensional manifolds along the phase adhesion genus of surfaces, the classification of incompressible surfaces in 3D manifolds, and the classification of knot are the three core problems in the theory of three dimensional manifolds.In particular, the classification of incompressible surfaces in 3D manifolds is very important for studying the genus additivity of 3D manifolds and the classification of knots.In this paper, a series of sufficient conditions for some simple perforated spherical surfaces and genus additivity of closed surface I-bundle are given by studying the sum of three perforated spherical surfaces of closed surface and the special type of perforated spherical surface of closed surface I-bundle.Based on the results of simple perforated spherical surfaces of closed surface I-bundle and genus additivity, this paper analyses and discusses the problem of complex three-dimensional manifold perforated sphere and whether it has genus additivity or not.In this paper, the sufficient conditions for some complex three-dimensional manifolds to be simple with edges and have genus additivity are given.That is, if Mi is a compact, orientable three-dimensional manifold F _ I is an incompressible curved surface with edges on the boundary of Mi ~ (2) is a homeomorphism from F _ 1 to F _ 2.For a phase viscous surface with specific conditions, if Mi has a Heegaard decomposition with a Heegaard distance of at least 2g / M _ (1) / g / M _ 2N _ 1, then I / M _ (1) / g / M _ (1) / g / M _ (2) ~ (2).
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O189.3

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