论文标题
奇异空间的拓扑边界和对L级分层的应用
Topological Bordism of Singular Spaces and an Application to Stratified L-Classes
论文作者
论文摘要
构建了一种广义的传统界界理论，以便对于某些歧管同型分层集（MHSS; Quinn空间）同态异态不变的几何基本基级存在。该结构结合了三个想法：首先，与其仅在链接上限制几何循环，而是直接通过几何特性构建了更灵活的框架，其次，使用了受控的拓扑方法来给出一个基于链接的标准，以检测合适的循环，第三，几乎没有用于研究这些循环的几个类别，这些阶段适用于这些类别，这些类别interincient intimitient intimentic intincient intincient intincient intincient intincient intim intim intim intim intincient。作为应用程序，我们在MHSS WITT空间上为链路上的条件和会议阶层的维度间距提供了拓扑（同构）不变（同源性）L级别的构造。每当这些空间与戈尔斯基·麦克弗森（Goresky-Macpherson L-Classes）与PL-peSudomanifolds相同时，这些L级别同意。
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly, instead of restricting geometric cycles by conditions on links only, a more flexible framework is built directly via geometric properties, secondly, controlled topology methods are used to give an accessible link-based criterion to detect suitable cycles and thirdly, a geometric argument is used to show, that these classes of cycles are suitable to study the transition to intrinsic stratifications. As an application, we give a construction of topologically (homeomorphism) invariant (homological) L-classes on MHSS Witt-spaces satisfying conditions on Whitehead-groups of links and the dimensional spacing of meeting strata. These L-classes agree, whenever those spaces are additionally pl-pseudomanifolds, with the Goresky-MacPherson L-classes.
