论文标题
通过链接和Stein分解的规律性
Regularity via Links and Stein Factorization
论文作者
论文摘要
在这里，我们介绍了在组合（PL三角形）歧管上的分段线性（PL）函数的常规点的新定义。此定义是根据函数限制到点链路的限制给出的。我们表明，我们对规律性的定义与组合拓扑文献中存在的其他定义不同。接下来，我们将此类地图的Jacobi集/关键位点分类为POSET分层空间。作为应用程序，我们考虑了PL功能的REEB空间，将REEB空间和函数的目标分层，并表明Stein分解是分层空间的映射。
Here, we introduce a new definition of regular point for piecewise-linear (PL) functions on combinatorial (PL triangulated) manifolds. This definition is given in terms of the restriction of the function to the link of the point. We show that our definition of regularity is distinct from other definitions that exist in the combinatorial topology literature. Next, we stratify the Jacobi set/critical locus of such a map as a poset stratified space. As an application, we consider the Reeb space of a PL function, stratify the Reeb space as well as the target of the function, and show that the Stein factorization is a map of stratified spaces.
