余维1芽和Morse函数扩张的简单性
Simplicity of augmentations of codimension 1 germs and by Morse functions
摘要：
我们研究的简单性的映射芽获得的操作的增强，并描述如何获得他们的cross-unfoldings。当增广来自于$\mathscr{A}_e$ -余维1芽或增广函数是Morse函数时，为了简单起见，我们给出了一个完整的刻画。这些特征在所有明确获得的$\mathscr{A}$分类中产生了所有简单的扩增-简单的单体，除了一个（Mond列表中的$F_4$从$\mathbb{C}^2$到$\mathbb{C}^3$）。此外，使用我们的结果，我们产生了一个列表的简单的增广从$\mathbb{C}^4$到$\mathbb{C}^4$。
英文摘要：
We study the simplicity of map-germs obtained by the operation of augmentation and describe how to obtain their versal unfoldings. When the augmentation comes from an $\mathscr{A}_e$-codimension 1 germ or the augmenting function is a Morse function, we give a complete characterisation for simplicity. These characterisations yield all the simple augmentations in all explicitly obtained classifications of $\mathscr{A}$-simple monogerms except for one ($F_4$ in Mond's list from $\mathbb{C}^2$ to $\mathbb{C}^3$). Moreover, using our results we produce a list of simple augmentations from $\mathbb{C}^4$ to $\mathbb{C}^4$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
