论文标题
ICI的同源性和MAP细菌变形的图像的同型组成部分
Isotypical components of the homology of ICIS and images of deformations of map germs
论文作者
论文摘要
我们提供了一种简单的方法来研究与有限基团的作用的简单复合物同源性的同种异体组成部分，并将其用于ICIS的Milnor纤维。我们研究映射$ f_t $的图像的同源性，这些图像作为复杂地图细菌的变形$ f：（\ mathbb {c}^n，s）\ to（\ mathbb {c}^p，0）$，带有$ n <p $，以及在此上下文中具有奇异性（Insunluce）的行为。我们研究了Mond给出的图像Milnor数字$μ_i$的两个概括，并提供了一种可行的方式，以corank One和Milnor数量ICI的数量计算它们。当$ p> n+1 $：稳定的扰动和$ \ text {im} f_t $在意外的维度中，我们还研究两个意外特征。我们表明，休斯顿的猜想，$μ_i$在一个家庭中的常数意味着在加夫尼意义上是错误的，但我们对猜想的陈述进行了正确的修改，我们也证明了这一点。
We give a simple way to study the isotypical components of the homology of simplicial complexes with actions of finite groups, and use it for Milnor fibers of ICIS. We study the homology of images of mappings $f_t$ that arise as deformations of complex map germs $f:(\mathbb{C}^n,S)\to(\mathbb{C}^p,0)$, with $n<p$, and the behaviour of singularities (instabilities) in this context. We study two generalizations of the notion of image Milnor number $μ_I$ given by Mond and give a workable way of compute them, in corank one, with Milnor numbers of ICIS. We also study two unexpected traits when $p>n+1$: stable perturbations with contractible image and homology of $\text{im} f_t$ in unexpected dimensions. We show that Houston's conjecture, $μ_I$ constant in a family implies excellency in Gaffney's sense, is false, but we give a correct modification of the statement of the conjecture which we also prove.
