论文标题
编码1种细菌和通过摩尔斯的功能的增强的简单性
Simplicity of augmentations of codimension 1 germs and by Morse functions
论文作者
论文摘要
我们研究了通过增强操作获得的MAP-GERM的简单性，并描述了如何获得其广泛展开的方式。当增强来自$ \ mathscr {a} _e $ -sodimension 1 grem或增强功能是morse函数时，我们为简单起见提供完整的表征。这些特征在所有明确获得的$ \ mathscr {a} $的分类中产生了所有简单的增强 - 简单的单凝胶除外（一个$ f_4 $ in mond列表中的$ \ m \ m m i \ mathbb {c}^2 $ to $ \ mathbb {c}^$ \ mathbb {c}^3 $）。此外，使用我们的结果，我们从$ \ mathbb {c}^4 $到$ \ MATHBB {C}^4 $制作了简单增强列表。
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 $\mathbb{C}^4$.
