Recognition Problem in Singularity Theory of Differentiable Mappings

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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.