Transfer Maps and Orientation Classes of Singular Spaces

奇异空间的传递图和方向类

• 批准号: 495696766
• 负责人: Professor Dr. Markus Banagl
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/495696766?language=en
• 关键词: Transfer; Maps; Orientation; Classes; Singular

The confluence of topological methods such as L-theory, intersection homology and ad-theories, complex algebraic methods coming from the theory of mixed Hodge modules, and global real analytic methods involving iterated edge Riemannian metrics and K-homology, has recently lead to the construction of a dense portfolio of orientation and characteristic classes for singular spaces that often generalize classical invariants of manifold theory. Understanding the behavior of these classes under various topological and algebraic Gysin restrictions, bundle transfer maps and pullback under smooth algebraic morphisms begins to emerge as a key to computability and applicability. The project thus aims for discerning and establishing the basic transformational laws governing orientation classes of singular spaces under transfers on several relevant homology theories such as bordism, K- and L-homology. The results are expected to impact existing conjectures concerning the relation of the invariants to each other. The laws found will then provide the foundation of new computational methods for concrete types of singular spaces, particularly projective varieties beyond rational homology manifolds, e.g. for Schubert varieties and other varieties arising in mathematical Physics.

L 理论、交同调和 ad 理论等拓扑方法、来自混合 Hodge 模理论的复杂代数方法以及涉及迭代边缘黎曼度量和 K 同调的全局实分析方法的融合，最近导致了奇异空间方向和特征类的密集组合的构造，这些组合通常概括了流形理论的经典不变量。理解这些类在各种拓扑和代数 Gysin 限制下的行为、束传递映射和光滑代数态射下的回拉开始成为可计算性和适用性的关键。因此，该项目的目标是在几种相关的同调理论（如 Bordism、K-和 L-同调）上识别和建立控制奇异空间方向类的基本变换定律。预计结果将影响有关不变量之间关系的现有猜想。所发现的定律将为具体类型的奇异空间提供新的计算方法的基础，特别是超越有理同调流形的射影簇，例如用于舒伯特簇和数学物理学中出现的其他簇。