论文标题
相交同源和同型组之间的关系
Relation between intersection homology and homotopy groups
论文作者
论文摘要
由于Goresky和MacPherson交叉路口同源性不是空间的同源性，因此没有首选的候选人，用于相交的同型组。在这里，它们被定义为P. Gajer将其与一个过滤空间和变态的$ $（x，\ overline {p}）相关联的简单集的同副群。我们首先作为交叉基本组的一些基本属性作为范·坎佩（Van Kampen）定理。 对于Siebenmann CS集合的一般交叉点同质组，我们证明了它们与Goresky和MacPherson和MacPherson交叉点同源性之间的Hurewicz定理。如果CS设置及其固有分层具有相同的常规部分，我们将建立$ \叠加{p} $ - 相交同型组的拓扑不变性。几个例子证明了声明中提出的假设是合理的。最后，交点同拷贝组也与拓扑空间本身的同型组相吻合，在连接的正常thom妈妈空间上具有最高的变态。
As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to a couple $(X,\overline{p})$ of a filtered space and a perversity. We first establish some basic properties for the intersection fundamental groups, as a Van Kampen theorem. For general intersection homotopy groups on Siebenmann CS sets, we prove a Hurewicz theorem between them and the Goresky and MacPherson intersection homology. If the CS set and its intrinsic stratification have the same regular part, we establish the topological invariance of the $\overline{p}$-intersection homotopy groups. Several examples justify the hypotheses made in the statements. Finally, intersection homotopy groups also coincide with the homotopy groups of the topological space itself, for the top perversity on a connected, normal Thom-Mather space.
