关于奇点集类型的分类探究问题  

On the Classification of Singular Point Set Types

作　　者：闫傲寒 YAN Ao-han(School of Mathemafics and Computer Science,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学与计算机学院,吉林长春130000

出　　处：《通化师范学院学报》2023年第8期20-25,共6页Journal of Tonghua Normal University

摘　　要：文章对奇点集局部理论进行研究,讨论了从Rn→Rp的光滑映射f的奇点集分类问题.文章从三个方面进行探究,分别是Thom的一阶奇点集、Thom的二阶奇点集和特殊的高阶奇点集,并通过具体的例子对这几种不同的奇点集进行讨论,从而得到了奇点集的简单分类,也得到了Boardman符号和Boardman奇点的几个重要结果,可为后续讨论映射芽的开折及稳定映射芽的分类奠定一定基础.This paper focuses on the research of local theory of singularity set,The purpose of this paper is to discuss the point classification of singularities of smooth mapping f from Rn→Rp.This paper describes it from three aspects,namely,the first order singularity set,the second order singularity set,and special higher order singularities.Three different sets of singular points are discussed through specific examples.Thus,the simple classification of singular point set is obtained and some important results of Boardman symbols and Boardman singularities are introduced.It is helpful for readers to understand the knowledge point of singularity set,and it is convenient for readers to inquire and discuss.It is prepared for further discussion of the unfolding and stability of map germs.

关 键 词：Thom的一阶奇点集 Thom的二阶奇点集 高阶奇点集 Boardman奇点 

分 类 号：O175.12[理学—数学]