Recognition Problem in Singularity Theory of Differentiable Mappings

如果两个奇点的局部行为本质上相同，则称它们是等价的。虽然这个等价关系在“可微映射的奇点理论”中是非常重要的，但要给出一个在一般情况下有效的判据是相当困难的。给出一个在一般情况下有效的标准的问题被称为“识别问题”，在开始这项研究之前，本研究的主要投资者已经发现了一个新的有效的方法（简要说明在第一章）“识别问题”。他还发表了许多关于这种新方法的各种版本的论文。本研究的主要目的是推动上述新方法的进一步推广。7.b这样做，首席投资者采用了本研究的以下过程。通过解释他的新方法并将其应用于作品（简要说明在第2章至第7章）的合作者谁正在研究的各个方面的“奇点理论的微分映射”，首席投资者试图让他们理解他新方法的效用。2首席投资者还简要地解释了代数学中一个问题的进展从这个研究的角度来看，他从来没有注意到，当他开始这项研究。

Two singularities are said to be equivalent if their local behaviors are essentially same. Though this equibalent relation is very important in "Singularity Theory of Differentiable Mappings", it is quite difficult to give a criterion which is effective in general cases. The problem of giving an effective criterion which works well in general cases is called "Recognition Problem".Before starting this research, the head investor of this research has discovered a new effective method (brief explanation is given in chapter 1) for "Recognition Problem". He has also published many papers on various versions of this new method. The main purpose of this research is to forward a further spread of the above new method. 7.b do so, the head investor adopted the following process of this research.By explaining his new method and adapting it to works (brief explanations are in from chapter 2 to chapter 7) of cooperators who are studying various aspects of "Singularity Theory of Differentiable Mappings", the head investor try to let them comprehend utility of his new method.The head investor also adds a brief explanation of progress on one problem in algebraic geometry from a view point of this research, which he has never noticed when he started this research.