On The Functorialrily Of Stratified Desingularizations

Categorical Properties Of Smooth Unfoldings On Stratified Spaces

In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather pseudomanifold with arbitary finite length, through a new kind of intermediate desingularizations, the unbendings, which coincide with primary unfoldings in the simple case.

光滑图册分层空间、K同调定向与Gysin映射

Smooth atlas stratified spaces, K-Homology Orientations, and Gysin maps

该研究引入光滑图册分层空间并证明其与Thom-Mather分层空间等价，在双变KK-理论中构造定向Witt分层空间纤维丛的Gysin映射并证明其保持解析符号差类，还建立了解析符号差类与拓扑Siegel-Sullivan定向的联系。