等变映射芽在左右等价群下的通用开折  

Versal unfolding of equivariant map-germs under left-right equivalence group

作　　者：李瑞雪 LI Rui-xue(Jilin Normal University,Siping 136000 China)

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《新余学院学报》2022年第2期27-35,共9页Journal of Xinyu University

摘　　要：对映射芽同时引进对称性和左右等价群,借助光滑映射奇点理论中的左右等价定义等变映射芽,研究紧致Lie群作用下的等变映射芽及其通用开折,给出了这种情况下等变映射芽的开折是通用开折的充要条件,并给出了相应的推论。The symmetry and the left-right equivalence group are introduced into map-germs at the same time.Using the left-right equivalence of the singularity theory of smooth mapping to define equivariant map-germs,this paper studies the equivariant map-germs and its versal unfolding under the action of compact Lie group.In this case,this paper concludes that the unfolding of the equivariant map-germs is the necessary and sufficient condition for its versal unfolding,and gives the corresponding inferences.

关 键 词：映射芽 通用开折 左右等价 对称性 

分 类 号：O192[理学—数学]