关于正规层伪流形
On Normal Stratified Pseudomanifolds
摘要：
一个分层伪流形是正规的，如果它的链路是连通的。分层伪流形$X$的归一化是正常分层伪流形$Y$连同满足与纤维相关的局部条件的有限对一投影$n:Y\to X$。映射n保持交同调。在Borel之后，任何pl-分层伪流形都有上述意义上的归一化。在这篇文章中：1.我们证明了映射$n$可以被要求满足一个更强的条件：它是一个局部平凡的分层态射保持圆锥结构横向于地层。2.-我们推广Borel的结果，任何拓扑分层pseudomanifold和一个家庭的persons这是大于通常的。3.-我们对这种规范化进行了明确的构建。我们给出了一个详细的描述规范化的分层。4.-我们证明，我们的建设是函，从而唯一的同构。我们的程序也适用于$C^{\infty}$类别，只需稍作调整。
英文摘要：
A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition related to the fibers. The map n preserves the intersection homology. Following Borel any pl-stratified pseudomanifod has a normalization in the above sense. In this parper: 1.- We prove that the map $n$ can be required to satisfy a stronger condition: it is a locally trivial stratified morphism preserving the conical structure transverse to the strata. 2.- We extend Borel's result for any topological stratified pseudomanifold and for a family of perversities which is larger than the usual one. 3.- We make an explicit construction of such a normalization. We give a detailed description of the normalizer's stratification. 4.- We prove that our construction is functorial, thus unique up to isomorphisms. With little adjust our procedure holds also in the $C^{\infty}$ category.
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