论文标题
奇异相交同源性维度的合理概念
A reasonable notion of dimension for singular intersection homology
论文作者
论文摘要
M. Goresky和R. MacPherson交叉路口同源性也是由H. King的单数链复合物定义的，并具有关键公式，可在单纯的单纯词之间进行选择。该公式需要一个欧几里得单纯形的子空间$ s $的尺寸概念，通常将其视为包含〜$ s $的骨架的最小尺寸。后来，P。Gajer根据包含$ S $的Polyhedra的维度采用了另一个维度。最后一个允许在奇异单纯形域内的奇异层的回调痕迹。 在这项工作中，我们证明了Siebenmann的CS集合的两个相应的相交同源物是同构。就金的论文而言，这意味着多面体维度是``合理''维度。该证明使用需要适应细分的Mayer-Vietoris参数。对于多面体维度，这是一个微妙的问题。一般立场论点还不够，我们引入了强大的一般立场。借助它，稳定性将添加到通用字符中，我们可以对每个单纯的单纯形进行电感切割。这种分解是通过伪 - 巴里式分区实现的，在这些细分中，新顶点不是barycentres，而是它们的近距离点。
M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for subspaces $S$ of a Euclidean simplex, which is usually taken as the smallest dimension of the skeleta containing~$S$. Later, P. Gajer employed another dimension based on the dimension of polyhedra containing $S$. This last one allows traces of pullbacks of singular strata in the interior of the domain of a singular simplex. In this work, we prove that the two corresponding intersection homologies are isomorphic for Siebenmann's CS sets. In terms of King's paper, this means that polyhedral dimension is a ``reasonable'' dimension. The proof uses a Mayer-Vietoris argument which needs an adaptated subdivision. With the polyhedral dimension, that is a subtle issue. General position arguments are not sufficient and we introduce strong general position. With it, a stability is added to the generic character and we can do an inductive cutting of each singular simplex. This decomposition is realised with pseudo-barycentric subdivisions where the new vertices are not barycentres but close points of them.
