Topological Invariants of Stratified Spaces
Topological Invariants of Stratified Spaces
复制标题
分层空间的拓扑不变量
DOI：
10.1007/3-540-38587-8
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发表时间：
2007
影响因子：
3.1
通讯作者：
Markus Banagl
中科院分区：
文献类型：
--
作者：
Markus Banagl
这本书的中心主题是恢复庞加莱对偶分层奇异空间使用维迪尔自对偶层，如原型交叉链层的复杂品种。
在仔细介绍了层理论、派生范畴、Verdier对偶、分层理论、交同调、t-结构和反常层之后，最终目标是解释自对偶层实现的签名和特征类等不变量的构造以及代数和几何性质。
亮点从来没有在书中提出的形式包括完整和非常详细的证明分解定理的自对偶层，解释方法计算扭曲的特征类和介绍作者的理论的非维特空间和拉格朗日结构。
The central theme of this book is the restoration of Poincare duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety.
After carefully introducing sheaf theory, derived categories, Verdier duality, stratification theories, intersection homology, t-structures and perverse sheaves, the ultimate objective is to explain the construction as well as algebraic and geometric properties of invariants such as the signature and characteristic classes effectuated by self-dual sheaves.
Highlights never before presented in book form include complete and very detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.